Name: ________________________ Class: ___________________ Date: __________ ID: A

1

AP Stats Midterm Review

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

1 If the individual outcomes of a phenomenon are uncertain, but there is nonetheless a regular distribution of outcomes in a large number of repetitions, we say the phenomenon isA random.B predictable.C uniform.D probable.E normal.

Scenario 1-4Mr. Williams asked the 26 seniors in his statistics class how many A.P. courses they had taken during high school. Below is a dot plot summarizing the results of his survey.

2 Use Scenario 1-4. The median number of A.P. courses taken by Mr. Williams’s students isF 2G 3H 3.5J 4K cannot be determined from the information

given.

3 Use Scenario 1-4. The interquartile range for the number of A.P. Courses isA 3 to 4B 2.5 to 5C 3 to 5D 2E 2.5

Name: ________________________ ID: A

2

4 Use Scenario 1-4. Which of the following is a correct box plot for these data?

F AG BH CJ DK E

Scenario 5-1To simulate a toss of a coin we let the digits 0, 1, 2, 3, and 4 correspond to a head and the digits 5, 6, 7, 8, and 9 correspond to a tail. Consider the following game: We are going to toss the coin until we either get a head or we get two tails in a row, whichever comes first. If it takes us one toss to get the head we win $2, if it takes us two tosses we win $1, and if we get two tails in a row we win nothing. Use the following sequence of random digits to simulate this game as many times as possible:12975 13258 45144

5 Use Scenario 5-1. Based on your simulation, the estimated probability of winning $2 in this game isA 1/4.B 5/15.C 7/15.D 9/15.E 7/11.

6 Use Scenario 5-1. Based on your simulation, the estimated probability of winning nothing isF 1/2.G 2/11.H 2/15.J 6/15.K 7/11.

7 Using the standard Normal distribution tables, the area under the standard Normal curve corresponding to Z < 1.1 isA 0.1357.B 0.2704.C 0.8413.D 0.8438.E 0.8643.

Name: ________________________ ID: A

3

8 The histogram below show the length (in minutes) of 140 songs recorded by the band Wilco.

Which of the following descriptions best fits this distribution?F Skewed right, centered at about 8, with several high outliers.G Skewed left, centered at about 8, with several high outliers.H Skewed right, centered at about 4.5, with several high outliers.J Skewed left, centered at about 4.5, with several high outliers.K Skewed left, centered at about 3.5, with several high outliers.

Scenario 5-2If you draw an M&M candy at random from a bag of the candies, the candy you draw will have one of six colors. The probability of drawing each color depends on the proportion of each color among all candies made. The table below gives the probability that a randomly chosen M&M had each color before blue M & M’s replaced tan in 1995.

Color Brown Red Yellow Green Orange TanProbability 0.3 0.2 ? 0.1 0.1 0.1

9 Use Scenario 5-2. The probability that you draw either a brown or a green candy isA .1.B .3.C .4.D .6.E .7.

10 Use Scenario 5-2. The probability that you do not draw a red candy isF .2.G .3.H .7.J .8.K impossible to determine from the information

given.

11 Use Scenario 5-2. The probability of drawing a yellow candy isA 0.B .1.C .2.D .3.E impossible to determine from the information

given.

Name: ________________________ ID: A

4

Scenario 4-5In order to assess the effects of exercise on reducing cholesterol, a researcher took a random sample of fifty people from a local gym who exercised regularly and another random sample of fifty people from the surrounding community who did not exercise regularly. They all reported to a clinic to have their cholesterol measured. The subjects were unaware of the purpose of the study, and the technician measuring the cholesterol was not aware of whether or not subjects exercised regularly.

12 Use Scenario 4-5. Which of the following best describes the inferences the researcher can make based in his results?F He can make inferences about cause and

effect, but not about the populations from which the samples were taken.

G He can make inferences about the populations from which the samples were taken, but not about cause and effect.

H He can make inferences about both cause and effect and the populations from which the samples were taken.

J He cannot make inferences about either cause and effect or the populations from which the samples were taken.

K There is not enough information to make judgments about the scope of inference.

13 Use Scenario 4-5. This is a(n)A observational study.B experiment, but not a double blind

experiment.C double blind experiment.D matched pairs experiment.E block design.

14 Suppose that A and B are independent events

with and .

is

F 0.08.G 0.12.H 0.40.J 0.52.K 0.60.

15 A set of 10 cards consists of 5 red and 5 black cards. The cards are shuffled thoroughly and you turn cards over, one at a time, beginning with the top card. Let Y be the number of cards you turn over until you observe the first red card. The random variable Y has which of the following probability distributions?

A Normal with a mean of 5B binomial with p = 0.5C geometric with p = 0.5D uniform with value 1 from 0 to 1E none of the above

Name: ________________________ ID: A

5

Figure 1-1

16 Use Figure 1-1. The mean of this histogram is approximatelyF 70 inches.G 74 inches.H 78 inches.J 82 inches.K 86 inches.

17 Use Figure 1-1. Based on this histogram, the percentage of the winning jumps that were at least 80 inches is aboutA 10%.B 35%.C 45%.D 55%.E 90%.

18 Use Figure 1-1. For these data,F the median jump is between 75 and 80

inches.G the median jump is between 80 and 85

inches.H the smallest jump must be below 65 inches.J the winning jump in the 1976 Olympic

Games was 40 inches.K none of the above.

19 The essential difference between an experiment and an observational study is thatA observational studies may have confounded

variables, but experiments never do.B in an experiment, people must give their

informed consent before being allowed to participate.

C observational studies are always biased.D observational studies cannot have response

variables.E an experiment imposes treatments on the

subjects, but an observational study does not.

Name: ________________________ ID: A

6

Scenario 5-8A student is chosen at random from the River City High School student body, and the following events are recorded:M = The student is maleF = The student is femaleB = The student ate breakfast that morning.N = The student did not eat breakfast that morning.The following tree diagram gives probabilities associated with these events.

20 Use Scenario 5-8. Find and write in

words what this expression represents.F 0.18; The probability the student ate

breakfast and is female.G 0.18; The probability the student ate

breakfast, given she is female.H 0.18; The probability the student is female,

given she ate breakfast.J 0.30; The probability the student ate

breakfast, given she is female.K 0.30; The probability the student is female,

given she ate breakfast.

21 Use Scenario 5-8. What is the probability that the student had breakfast?A 0.32B 0.40C 0.50D 0.64E 0.80

22 Use Scenario 5-8. What is the probability that the selected student is a male and ate breakfast?F 0.32G 0.40H 0.50J 0.64K 0.80

23 Use Scenario 5-8. Given that a student who ate breakfast is selected, what is the probability that he is male?A 0.32B 0.40C 0.50D 0.64E 0.80

Name: ________________________ ID: A

7

Scenario 3-1The height (in feet) and volume (in cubic feet) of usable lumber of 32 cherry trees are measured by a researcher. The goal is to determine if volume of usable lumber can be estimated from the height of a tree.

24 Use Scenario 3-1. If the data point (65,70) were removed from this study, how would the value of the correlation r change?F r would be smaller, since there are fewer data

points.G r would be smaller, because this point falls in

the pattern of the rest of the data.H r would be larger, since the x and y

coordinates are larger than the mean x and mean y, respectively.

J r would be larger, since this point does not fall in the pattern of the rest of the data.

K r would not change, since it’s value does not depend which variable is used for x and which is used for y.

25 Use Scenario 3-1. Which of the following statements are supported by the scatterplot? I. There is a positive association between height and volume. II. There is an outlier in the plot. III. As the height of a cherry tree increases, the volume of useable lumber it yields increases.A I onlyB II onlyC III onlyD I and IIE I, II, and III

26 Use Scenario 3-1. In this study, the response variable isF height of researcher.G volume of lumber.H height of tree.J the measuring instrument used to measure

volume.K impossible to determine.

Name: ________________________ ID: A

8

Scenario 1-2Below is a two-way table summarizing the number of cylinders in selected car models manufactured in six different countries in the 1990’s.

Number of cylinders4 5 6 8 Total

France 0 0 1 0 1Germany 4 1 0 0 5

Italy 1 0 0 0 1Japan 6 0 1 0 7

Sweden 1 0 1 0 2U.S.A. 7 0 7 8 22

Total 19 1 10 8 38

27 Use Scenario 1-2. Which of the following is a marginal distribution?A The percentage of all four-cylinder cars

manufactured in Germany.B The number of four-cylinder cars

manufactured in Germany.C The percentage of all cars manufactured in

each country.D The percentage of cars manufactured in

Germany for each number of cylinders.E The numbers 4, 5, 6, 8.

28 Use Scenario 1-2. The percent of cars with 4-cylinder engines that are made in Germany isF 10.5%.G 21%.H 50%.J 80%.K 91%.

29 Use Scenario 1-2. The percentage of all cars listed in the table with 4-cylinder engines isA 19%.B 21%.C 50%.D 80%.E 91%.

30 Use Scenario 1-2. From this table, we might conclude thatF there is a strong association between country

of origin and number of cylinders.G about 18% of the cars sold in the United

States were manufactured in Japan.H these data could be more effectively

presented with a box plot.J the only eight cylinder cars in this data set

were manufactured in Germany.K All the cars on Italian roads have four

cylinders.

31 An example of a nonsampling error that can reduce the accuracy of a sample survey isA using voluntary response to choose the

sample.B using the telephone directory as the sampling

frame.C interviewing people at shopping malls to

obtain a sample.D variation due to chance in choosing a sample

at random.E many members of the sample cannot be

contacted.

Name: ________________________ ID: A

9

Scenario 5-11The following table compares the hand dominance of 200 Canadian high-school students and what methods they prefer using to communicate with their friends.

Cell phone/Text In person Online TotalLeft-handed 12 13 9 34Right-handed 43 72 51 166

Total 55 85 60 200

Suppose one student is chosen randomly from this group of 200.

32 Use Scenario 5-11. If you know the person that has been randomly selected is left-handed, what is the probability that they prefer to communicate with friends in person?F 0.065G 0.153H 0.17J 0.382K 0.53

33 Use Scenario 5-11. What is the probability that the student chosen is left-handed or prefers to communicate with friends in person?A 0.065B 0.17C 0.425D 0.53E 0.595

34 A set of data has a mean that is much larger than the median. Which of the following statements is most consistent with this information?F The distribution is symmetric.G The distribution is skewed left.H The distribution is skewed right.J The distribution is bimodal.K The data set probably has a few low outliers.

35 Suppose there are three cards in a deck, one marked with a 1, one marked with a 2, and one marked with a 5. You draw two cards at random and without replacement from the deck of three cards. The sample space S = {(1, 2), (1, 5), (2, 5)} consists of these three equally likely outcomes. Let X be the sum of the numbers on the two cards drawn. Which of the following is the correct set of probabilities for X?

(A) X P(X) (B) X P(X) (C) X P(X) (D) X P(X) (E) X P(X)1 1/3 3 1/3 3 3/16 3 1/4 1 1/42 1/3 6 1/3 6 6/16 6 1/2 2 1/25 1/3 7 1/3 7 7/16 7 1/2 5 1/2

A AB BC CD DE E

Name: ________________________ ID: A

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36 The principle reason for the use of random assignment in designing experiments is that itF distinguishes a treatment effect from the

effects of confounding variables.G allows double-blinding.H reduces sampling variability.J creates approximately equal groups for

comparison.K eliminates the placebo effect.

37 Items produced by a manufacturing process are supposed to weigh 90 grams. The manufacturing process is such, however, that there is variability in the items produced and they do not all weigh exactly 90 grams. The distribution of weights can be approximated by a Normal distribution with mean 90 grams and a standard deviation of 1 gram. About what percentage of the items will either weigh less than 87 grams or more than 93 grams?A 0.15%B 0.3%C 6%D 94%E 99.7%

38 A stratified random sample addresses the same issues as which of the following experimental designs?F A block design.G A double-blind experiment.H An experiment with a placebo.J A matched pairs design.K A confounded, nonrandomized study.

39 You catch 10 cockroaches in your bedroom and measure their lengths in centimeters. Which of these sets of numerical descriptions are all measured in centimeters?A median length, variance of lengths, largest

lengthB median length, first and third quartiles of

lengthsC mean length, standard deviation of lengths,

median lengthD mean length, median length, variance of

lengths.E both (B) and (C)

40 The median age of five elephants at a certain zoo is 30 years. One of the elephants, whose age is 50 years, is transferred to a different zoo. The median age of the remaining four elephants isF 40 years.G 30 years.H 25 years.J less than 30 years.K Cannot be determined from the information

given.

Name: ________________________ ID: A

11

Scenario 3-7

Below is a scatter plot (with the least squares regression line) for calories and protein (in grams) in one cup of 11 varieties of dried beans. The computer output for this regression is below the plot.

41 Use Scenario 3-7. Which of the following statements is a correct interpretation of the slope of the regression line?A For each 1-unit increase in the calorie

content, the predicted protein content increases by 2.08 grams.

B For each 1-unit increase in the calorie content, the predicted protein content increases by 0.063 grams.

C For each 1-gram increase in the protein content, the predicted calorie content increases by 2.08 grams.

D For each 1-gram increase in the protein content, the predicted calorie content increases by 0.063 grams.

E For each 1-gram increase in the protein content, the predicted calorie content increases by 0.024 grams.

42 Use Scenario 3-7. Which of the following best describes what the number S = 3.37648 represents?F The slope of the regression line is 3.37648.G The standard deviation of the explanatory

variable, calories, is 3.37648.H The standard deviation of the response

variable, protein content, is 3.37648.J The standard deviation of the residuals is

3.37648.K The ratio of the standard deviation of protein

to the standard deviation of calories is 3.37648.

43 Use Scenario 3-7. The circled point on the scatter plot represents lima beans, which have 621 calories and 37 grams of protein. The residual for lima beans is:A –37.0B –4.18C 4.18D 37.0E 41.18

Name: ________________________ ID: A

12

44 Use Scenario 3-7. One cup of dried soybeans contains 846 calories. Which of the following statements is appropriate?F We can predict that the protein content for

soybeans is 55.4 grams.G We can predict that the protein content for

soybeans is 53.3 gramsH We can predict that the protein content for

soybeans is 51.2 gramsJ Unless we are given the observed protein

content for soybeans, we can’t calculate the predicted protein content.

K It would be inappropriate to predict the protein content of soybeans with this regression model, since their calorie content is well beyond the range of these data.

45 A basketball player makes 2/3 of his free throws. To simulate a single free throw, which of the following assignments of digits to making a free throw are appropriate? I. 0 and 1 correspond to making the free throw and 2 corresponds to missing the free throw. II. 01, 02, 03, 04, 05, 06, 07, and 08 correspond to making the free throw and 09, 10, 11, and 12 correspond to missing the free throw. III. Use a die and let 1, 2, 3, and 4 correspond to making a free throw while 5 and 6 correspond to missing a free throw.A I onlyB II onlyC III onlyD I and IIIE I, II, and III

Scenario 4-8Researchers wish to determine if a new experimental medication will reduce the symptoms of allergy sufferers without the side effect of drowsiness. To investigate this question, the researchers randomly assigned 100 adult volunteers who suffer from allergies to two groups. They gave the new medication to the subjects in one group and an existing medication to the subjects in the other group. Forty-four percent of those in the treatment group and 28% of those in the control group reported a significant reduction in their allergy symptoms without any drowsiness.

46 Use Scenario 4-8. The experimental units are theF researchers.G 100 adult volunteers.H all the volunteers who reported a significant

reduction in their allergy symptoms without any drowsiness.

J all the volunteers who did not report a significant reduction in their allergy symptoms without any drowsiness.

K pills containing the new experimental medication.

47 Use Scenario 4-8. Which of the following best describes the inferences the researchers can make based in his results?A They can make inferences about cause and

effect, but not about the populations from which the samples were taken.

B They can make inferences about the populations from which the samples were taken, but not about cause and effect.

C They can make inferences about both cause and effect and the populations from which the samples were taken.

D They cannot make inferences about either cause and effect or the populations from which the samples were taken.

E There is not enough information to make judgments about the scope of inference.

Name: ________________________ ID: A

13

48 If 30 is added to every number on a list, the only one of the following that is not changed isF the mean.G the mode.H the 75th percentile.J the median.K the standard deviation.

49 Consider the scatter plot below for a very small data set, consisting of the heights of five fathers (x) and their

sons (y). The “M” in the plot indicates the point . The letters A – E are labels for the five father-son

pairs.

Which father-son pair contributes the largest positive quantity to the correlation between father and son heights?A Pair AB Pair BC Pair CD Pair DE Pair E

50 In an experiment, an observed effect so large that it would rarely occur by chance is calledF an outlier.G influential.H statistically significant.J bias.K replication.

51 You can roughly locate the mean of a density curve by eye because it isA the point at which the curve would balance if

made of solid material.B the point that divides the area under the curve

into two equal parts.C the point at which the curve reaches its peak.D the point where the curvature changes

direction.E the point at which the height of the graph is

equal to 1.

Name: ________________________ ID: A

14

Scenario 3-8

A fisheries biologist studying whitefish in a Canadian Lake collected data on the length (in centimeters) and egg production for 25 female fish. A scatter plot of her results and computer regression analysis of egg production versus fish length are given below.Note that Number of eggs is given in thousands (i.e., “40” means 40,000 eggs).

Predictor Coef SE Coef T PConstant -142.74 25.55 -5.59 0.000Fish length 39.250 5.392 7.28 0.000

S = 6.75133 R-Sq = 69.7% R-Sq(adj) = 68.4%

52 Use Scenario 3-8. Which of the following is the plot of residuals versus fish lengths?

F

G

H

Name: ________________________ ID: A

15

J

K

53 IQs among undergraduates at Mountain Tech are approximately Normally distributed. The mean undergraduate IQ is 110. About 95% of undergraduates have IQs between 100 and 120. The standard deviation of these IQs is aboutA 5.B 10.C 15.D 20.E 25.

54 Suppose that A and B are independent events

with and .

is:

F 0.08.G 0.12.H 0.44.J 0.52.K 0.60.

55 A public opinion poll in Ohio wants to determine whether or not registered voters in the state approve of a measure to ban smoking in all public areas. They select a simple random sample of fifty registered voters from each county in the state and ask whether they approve or disapprove of the measure. This is an example of aA systematic random sample.B stratified random sample.C multistage sample.D simple random sample.E cluster sample.

56 Suppose that scores on a certain IQ test are Normally distributed with mean 110 and standard deviation 15. Then about 40% of the scores are betweenF 80 and 140.G 65 and 155.H 106 and 110.J the 25th and 75th percentiles.K 102 and 118.

Scenario 5-7The probability of a randomly selected adult having a rare disease for which a diagnostic test has been developed is 0.001. The diagnostic test is not perfect. The probability the test will be positive (indicating that the person has the disease) is 0.99 for a person with the disease and 0.02 for a person without the disease.

57 Use Scenario 5-7. If a randomly selected person is tested and the result is positive, the probability the individual has the disease isA 0.001.B 0.019.C 0.020.D 0.021.E 0.047.

Name: ________________________ ID: A

16

58 Use Scenario 5-7. The proportion of adults for which the test would be positive isF 0.00002.G 0.00099.H 0.01998.J 0.02097.K 0.02100.

59 You are chatting with the principal of a local high school. The topic of SAT scores comes up, and the principal mentions that SAT scores at the school are Normally distributed. She doesn't remember the mean or the standard deviation, but she does remember that the upper and lower quartiles are 500 and 600. The standard deviation of SAT verbal scores is closest toA 25 points.B 50 points.C 75 points.D 100 points.E 550 points.

60 There are three children in a room, ages three, four, and five. If a four-year-old child enters the room theF mean age will stay the same but the variance

will increase.G mean age will stay the same but the variance

will decrease.H mean age and variance will stay the same.J mean age and variance will increase.K mean age and variance will decrease.

Scenario 4-2You want to know the opinions of American school teachers about establishing a national test for high school graduation. You obtain a list of the members of the National Education Association (the largest teachers' union) and mail a questionnaire to 2500 teachers chosen at random from this list. In all 1347 teachers return the questionnaire.

61 Use Scenario 4-2. The sampling frame isA the 1347 teachers who mail back the

questionnaire.B the 2500 teachers to whom you mailed the

questionnaire.C all members of the National Education

Association.D all American school teachers.E all American school students.

62 Use Scenario 4-2. The sample isF the 1347 teachers who mail back the

questionnaire.G the 2500 teachers to whom you mailed the

questionnaire.H all members of the National Education

Association.J all American school teachers.K all American school students.

63 Which of the following is not a major principle of good design for all experiments?A Comparison to a control.B ReplicationC BlockingD RandomizationE All of these are important principles for

every experiment.

Name: ________________________ ID: A

17

64 A data set is Normally distributed with a mean of 25 and a standard deviation of 8. If you calculate the standard score of every observation in this data set, the resulting scores will have a distribution that hasF a mean of 100 and a standard deviation of 10.G a mean of 25 and a standard deviation of 10.H a mean of 25 and a standard deviation of 1.J a mean of 1 and a standard deviation of 1.K a mean of 0 and a standard deviation of 1.

Scenario 4-3We wish to choose a simple random sample of size three from the following employees of a small company. To do this, we will use the numerical labels attached to the names below.

1. Bechhofer 4. Kesten 7. Taylor2. Brown 5. Kiefer 8. Wald3. Ito 6. Spitzer 9. Weiss

We will also use the following list of random digits, reading the list from left to right, starting at the beginning of the list.

11793 20495 05907 11384 44982 20751 27498 12009 45287 71753 98236 66419 84533

65 Use Scenario 4-3. Which of the following statements is true?A If we use another list of random digits to

select the sample, we would get the same result as that obtained with the list actually used.

B If we use another list of random digits to select the sample, we would get a completely different sample than that obtained with the list actually used.

C If we use another list of random digits to select the sample, we would get, at most, one name in common with that obtained with the list actually used.

D If we use another list of random digits to select the sample, the result obtained with the list actually used would be just as likely to be selected as any other set of three names.

E If we use another list of random digits to select the sample, the result obtained with the list actually used would be far less likely to be selected than any other set of three names.

66 Roll one 10-sided die 12 times. The probability of getting exactly 4 eights in those 12 rolls is given by

F 10

4

Ê

Ë

ÁÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃˜̃˜̃

• 110

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

4

• 910

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

8

G 10

4

Ê

Ë

ÁÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃˜̃˜̃

• 110

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

4

• 910

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

6

H 12

4

Ê

Ë

ÁÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃˜̃˜̃

• 110

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

4

• 910

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

6

J 12

4

Ê

Ë

ÁÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃˜̃˜̃

• 110

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

4

• 910

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

8

K 12

4

Ê

Ë

ÁÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃˜̃˜̃

• 110

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

8

• 910

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

4

Name: ________________________ ID: A

18

67 You read in a book on poker that the probability of being dealt three of a kind in a five-card poker hand is 1/50. What does this mean?A If you deal thousands of poker hands, the

fraction of them that contain three of a kind will be very close to 1/50.

B If you deal 50 poker hands, then one of them will contain three of a kind.

C If you deal 10,000 poker hands, then 200 of them will contain three of a kind.

D A probability of 0.02 is somebody’s best guess for a probability of being dealt three of a kind.

E It doesn’t mean anything, because 1/50 is just a number.

68 “Least-squares” in the term “least-squares regression line” refers toF Minimizing the sum of the squares of all

values of the explanatory variable.G Minimizing the sum of the squares of all

values of the response variable.H Minimizing the products of each value of the

response variable and the predicted value based on the regression equation.

J Minimizing the sum of the squares of the residuals.

K Minimizing the squares of the differences between each value of the response variable and each value of the explanatory variable.

69 Event A occurs with probability 0.3, and event B occurs with probability 0.4. If A and B are independent, we may conclude thatA P(A and B) = 0.12.B P(A|B) = 0.3.C P(B|A) = 0.4.D all of the above.E none of the above.

70 A poll conducted by the student newspaper asked, "Who do you believe will win the Ohio State Undergraduate Student Government elections?" In order to vote, one had to access the student newspaper's Web site and record one's vote. The results of the poll were summarized in a graphic similar to the following.

Which of the following statements is true about these results?F The results of the survey are unreliable

because response to the survey was voluntary.

G The sample is large enough to eliminate potential sources of bias in the design of the poll.

H This is not an appropriate way of presenting the results—a bar graph should have been used instead.

J Patel and Patel have such a large majority that, even though there are flaws in the poll, they are still almost certain to win.

K There must be an error. These percentages aren't possible.

71 Simple random samplingA reduces bias resulting from poorly worded

questions.B offsets bias resulting from undercoverage and

nonresponse.C reduces bias resulting from the behavior of

the interviewer.D reduces variability.E None of the above.

Name: ________________________ ID: A

19

72 Which of the following statements is not true?F If two events are mutually exclusive, they are

not independent.G If two events are mutually exclusive, then

= 0

H If two events are independent, then they must be mutually exclusive.

J If two events, A and B, are independent, then

K All four statements above are true.

73 A company produces ceramic floor tiles that are supposed to have a surface area of 16.0 square inches. Due to variability in the manufacturing process, the actual surface area has a Normal distribution with a mean of 16.1 square inches and a standard deviation of 0.2 square inches. The proportion of tiles produced by the process with surface area less than 16.0 square inches isA 0.1915.B 0.3085.C 0.3173.D 0.4115.E 0.6915.

74 In a study of the link between high blood pressure and cardiovascular disease, a group of white males aged 35 to 64 was followed for 5 years. At the beginning of the study, each man had his blood pressure measured and it was classified as either "low" systolic blood pressure (less than 140 mm Hg) or "high" blood pressure (140 mm Hg or higher). The following table gives the number of men in each blood pressure category and the number of deaths from cardiovascular disease during the 5-year period.

Blood pressure Deaths TotalLow 10 2000

High 5 3500

Based on these data, which of the following statements is correct?F These data are consistent with the idea that there is a link between high blood pressure

and death from cardiovascular disease.G The mortality rate (proportion of deaths) for men with high blood pressure is 5 times that

of men with low blood pressure.H These data probably understate the link between high blood pressure and death from

cardiovascular disease, because men will tend to understate their true blood pressure.J Although there were more deaths in the high blood pressure group, this is expected,

because there were 1500 more men in that group.K All of the above.

75 You would draw a scatterplot toA show the distribution of heights of students in this course.B compare the distributions of heights for male and female students in this course.C show the relationship between gender and having a driver’s license.D show the five-number summary for the heights of female students.E show the relationship between the height of female students and the heights of their

mothers.

Name: ________________________ ID: A

20

76 A policeman records the speeds of cars on a certain section of roadway with a radar gun. The histogram below shows the distribution of speeds for 251 cars.

Which of the following measures of center and spread would be the best ones to use when summarizing these data?F Mean and interquartile range.G Mean and standard deviation.H Median and range.J Median and standard deviation.K Median and interquartile range.

77 Consider the following cumulative relative frequency graph of the scores of students in an introductory statistics course:

A grade of C or C+ is assigned to a student who scores between 55 and 70. The percentage of students who obtained a grade of C or C+ is

A 15%B 20%C 25%D 30%E 50%

Name: ________________________ ID: A

21

Scenario 1-3For a physics course containing 10 students, the maximum point total for the quarter was 200. The point totals for the 10 students are given in the stemplot below.

11 6 8

12 1 4 8

13 3 7

14 2 6

15

16

17 9

78 Use Scenario 1-3. To which of the following data sets does this stemplot correspond?F All integers between 116 and 179G 1, 2, 3, 4, 6, 6, 7, 8, 8, 9H 16, 18, 21, 24, 28, 33, 37, 42, 46, 79J 116, 118, 121, 124, 128, 133, 137, 142, 146,

179K None of the above.

79 Use Scenario 1-3. This stemplot is most similar toA a histogram with class intervals 110 ≤ score

< 120, 120 ≤ score < 130, etc.B a time plot of the data with the observations

taken in increasing order.C a boxplot of the data.D reporting the 5 number summary for the data,

with the mean.E a dot plot of the data.

80 Use Scenario 1-3. The median point total for this class isF 130.G 130.5.H 133.J 134.4.K 137.

81 The principle reason for replication in designing experiments is that itA distinguishes a treatment effect from the

effects of confounding variables.B allows double-blinding.C reduces sampling variability.D creates approximately equal groups for

comparison.E eliminates the placebo effect.

82 The five-number summary of the distribution of scores on the final exam in Psych 001 last semester was:18 39 62 76 100

The 80th percentile was:F 76G between 18 and 39H between 62 and 76J between 76 and 100K probably between 39 and 76, since most of

the class scored between these two numbers.

Name: ________________________ ID: A

22

Scenario 3-2The following table and scatter plot present data on wine consumption (in liters per person per year) and death rate from heart attacks (in deaths per 100,000 people per year) in 19 developed Western countries.

Wine Consumption and Heart AttacksCountry Alcohol from

wineHeart disease deaths

Country Alcohol from wine

Heart disease deaths

Australia 2.5 211 Netherlands 1.8 167Austria 3.9 167 New Zealand 1.9 266Belgium 2.9 131 Norway 0.8 227Canada 2.4 191 Spain 6.5 86Denmark 2.9 220 Sweden 1.6 115Finland 0.8 297 Switzerland 5.8 285France 9.1 71 United

Kingdom1.3 199

Iceland 0.8 211 United States 1.2 172Ireland 0.7 300 West Germany 2.7Italy 7.9 107

83 Use Scenario 3-2. Do these data provide strong evidence that drinking wine actually causes a reduction in heart disease deaths?

Name: ________________________ ID: A

23

A Yes. The strong straight-line association in the plot shows that wine has a strong effect on heart disease deaths.

B No. Countries that drink lots of wine may differ in other ways from countries that drink little wine. We can't be sure the wine accounts for the difference in heart disease deaths.

C No. r does not equal –1.D No. The plot shows that differences among

countries are not large enough to be important.

E No. The plot shows that deaths go up as more alcohol from wine is consumed.

84 Use Scenario 3-2. The correlation between wine consumption and heart disease deaths is one of the following values. From the scatterplot, which must it be?F r = –0.84G r = –0.25H r is very close to 0J r = 0.25K r = 0.84

85 A particularly common question in the study of wildlife behavior involves observing contests between "residents" of a particular area and "intruders." In each contest, the "residents" either win or lose the encounter (assuming there are no ties). Observers might record several variables, listed below. Which of these variables is categorical?A The duration of the contest (in seconds).B The number of animals involved in the

contest.C Whether the "residents" win or lose.D The total number of contests won by the

"residents."E None of these.

Scenario 5-5Suppose we roll two six-sided dice--one red and one green. Let A be the event that the number of spots showing on the red die is three or less and B be the event that the number of spots showing on the green die is three or more.

86 Use Scenario 5-5. P(A ∩ B) =F 1/6.G 1/4.H 1/3.J 5/6.K none of these.

87 Use Scenario 5-5. The events A and B areA disjoint.B conditional.C independent.D reciprocals.E complementary.

88 Use Scenario 5-5. P(A ∪ B) =F 1/6.G 1/4.H 2/3.J 5/6.K 1.

89 Which of the following statements are true about the least-squares regression line? I. The slope is the predicted change in the response variable associated with a unit increase in the explanatory variable.II. The line always passes through the point (J , M ), the means of the explanatory and response variables, respectively.III. It is the line that minimizes the sum of the squared residuals.A I only.B II only.C III only.D I and III only.E I, II, and III are all true.

Name: ________________________ ID: A

24

90 If changes in a response variable are due to the effects of the explanatory variable as well as the effects of lurking variables, and we cannot distinguish between these effects, we are said to haveF a cause-and-effect relation between the

explanatory and response variable.G a placebo effect.H confounding.J correlation.K extrapolated.

91 Let the random variable X represent the weight of male black bears before they begin hibernation. Research has shown that the distribution of X is approximately Normal with a mean of 250 pounds and a standard deviation of 50 pounds What is P(X > 325 pounds)?

A 0.0668B 0.2514C 0.7486D 0.8531E 0.9332

92 A random sample of 100 students in grades 10 through 12 were sampled and asked their year in school and whether they were involved in interscholastic sports, intramural sports, or no sports. The results are summarized in the segmented bar graph below.

Based on this graph, which of the following statements is true?F More seniors are involved in interscholastic sports than sophomores.G There is no association between year in school and whether students are involved in

sports.H There were more seniors in the sample than juniors.J Juniors have the highest percentage participation in intramurals.K Less than half the seniors are involved in either interscholastic or intramural sports.

Name: ________________________ ID: A

25

93 Two variables are said to be negatively associated ifA larger values of one variable are associated

with larger values of the other.B larger values of one variable are associated

with smaller values of the other.C smaller values of one variable are associated

with smaller values of the other.D smaller values of one variable are associated

with both larger or smaller values of the other.

E there is no pattern in the relationship between the two variables.

94 You are playing a board game with some friends that involves rolling two six-sided dice. For eight consecutive rolls, the sum on the dice is 6. Which of the following statements is true?F Each time you roll another 6, the probability

of getting yet another 6 on the next roll goes down.

G Each time you roll another 6, the probability of getting yet another 6 on the next roll goes up.

H You should find another set of dice: eight consecutive 6’s is impossible with fair dice.

J The probability of rolling a 6 on the ninth roll is the same as it was on the first roll.

K None of these statements is true.

95 The correlation coefficient measuresA whether there is a relationship between two

variables.B the strength of the relationship between two

quantitative variables.C whether or not a scatterplot shows an

interesting pattern.D whether a cause and effect relation exists

between two variables.E the strength of the linear relationship

between two quantitative variables.

96 The principle reason for the use of controls in designing experiments is that itF distinguishes a treatment effect from the

effects of confounding variables.G allows double-blinding.H reduces sampling variability.J creates approximately equal groups for

comparison.K eliminates the placebo effect.

97 You open a package of plain M & M candies and count how many there are of each color. The distribution of the variable “candy color” is:A The colors: Red, Orange, Green, Yellow,

Brown, and Blue.B The total number of candies in the package.C Six—the number of different colors the are

in the package.D The six different colors and how many there

are of each.E Since “color” is a categorical variable, it

doesn’t have a distribution.

98 A factory makes silicon chips for use in computers. It is known that about 90% of the chips meet specifications. Every hour a sample of 18 chips is selected at random for testing and the number of chips that meet specifications is recorded. What is the approximate mean and standard deviation of the number of chips meeting specification?

F µ = 1.62; σ = 1.414G µ = 1.62; σ = 1.265H µ = 16.2; σ = 1.62J µ = 16.2; σ = 1.273K µ = 16.2; σ = 4.025

Name: ________________________ ID: A

26

99 Which of the following dot plots would best be approximated by a Normal distribution?

A AB BC CD DE E

100 The plot shown below is a Normal probability plot for the total annual cost (tuition plus room and board). to attend 126 of the top colleges in the country in 2005. Which statement is true for these data?

F The data are clearly Normally distributed.G The data are approximately Normally distributed.H The data are clearly skewed to the left.J The data are clearly skewed to the right.K There is insufficient information to determine the shape of the distribution.

Name: ________________________ ID: A

27

Scenario 3-3Consider the following scatterplot, which describes the relationship between stopping distance (in feet) and air temperature (in degrees Centigrade. for a certain 2,000-pound car travelling 40 mph.

101 Use Scenario 3-3. The correlation between temperature and stopping distanceA is approximately 0.9.B is approximately 0.6.C is approximately 0.0.D is approximately -0.6.E cannot be calculated, because some of the x

values are negative.

102 The mean number of days that the midge Chaoborus spends in its larval stage is 14.1 days, with a standard deviation of 2.2 days. This distribution is skewed toward higher values. What is the z-score for an individual midge that spends 12.7 days in its larval stage?F –1.11G –0.64H 0.64J 0.94K None of these, because z-score cannot be

used unless the distribution is Normal.

103 A stack of four cards contains two red cards and two black cards. I select two cards, one at a time, and do not replace the first card selected before selecting the second card. Consider the events

A = the first card selected is redB = the second card selected is red

The events A and B areA independent and disjoint.B not independent, but disjoint.C independent, not disjointD not independent, not disjoint.E independent, but we can’t tell it’s disjoint

without further information.

104 The table below shows the results of the New Hampshire Democratic Presidential Primary on January 8, 2008.

Candidate Percentage of votesHillary Clinton 39Barack Obama 37John Edwards 17

Bill Richardson 5Other 2

Which of the following lists of graphs are all appropriate ways of presenting these data?F Bar graph, Pie Chart, Box plotG Bar graph, Box plotH Bar graph, Pie ChartJ Bar Graph onlyK Pie Chart only

ID: A

1

AP Stats Midterm ReviewAnswer Section

MULTIPLE CHOICE

1 ANS: A PTS: 1 TOP: Idea of randomness

2 ANS: G PTS: 1 TOP: Medina from dot plot

3 ANS: D PTS: 1 TOP: IQR from dot plot

4 ANS: G PTS: 1 TOP: Box plot from dot plot

5 ANS: E PTS: 1 TOP: Simulation to estimate probability

6 ANS: G PTS: 1 TOP: Simulation to estimate probability

7 ANS: E PTS: 1 TOP: Standard Normal Calculations

8 ANS: H PTS: 1 TOP: Describing distribution; interpreting histogram

9 ANS: C PTS: 1 TOP: Addition of disjoint events

10 ANS: J PTS: 1 TOP: Complement rule

11 ANS: C PTS: 1 TOP: Basic Probability Rules

12 ANS: G PTS: 1 TOP: Scope of inference

13 ANS: A PTS: 1 TOP: Experiment vs. Observational study

14 ANS: G PTS: 1 TOP: Multiplication Rule, Independent events; Complement

15 ANS: C PTS: 1

16 ANS: J PTS: 1 TOP: Interpret histogram

17 ANS: D PTS: 1 TOP: Interpret histogram

18 ANS: G PTS: 1 TOP: Interpret histogram

19 ANS: E PTS: 1 TOP: Experiment vs. Observational study

20 ANS: J PTS: 1 TOP: Probabilities from tree diagram

21 ANS: C PTS: 1 TOP: Probabilities from tree diagram

22 ANS: F PTS: 1 TOP: Probabilities from tree diagram

23 ANS: D PTS: 1 TOP: Probabilities from tree diagram

24 ANS: J PTS: 1 TOP: Impact of Outlier on r

25 ANS: E PTS: 1 TOP: Interpreting Scatterplot

26 ANS: G PTS: 1 TOP: Explanatory/response

27 ANS: C PTS: 1 TOP: Marginal distribution-identification

28 ANS: G PTS: 1 TOP: Conditional distribution--calculation

29 ANS: C PTS: 1 TOP: Marginal distribution-calculation

30 ANS: F PTS: 1 TOP: Interpret two-way table

31 ANS: E PTS: 1 TOP: Non-sampling error

32 ANS: J PTS: 1 TOP: Conditional probability from 2-way table

33 ANS: D PTS: 1 TOP: Conditional probability from 2-way table

34 ANS: H PTS: 1 TOP: Mean, median, and skew

ID: A

2

35 ANS: B PTS: 1 TOP: Sample space

36 ANS: J PTS: 1 TOP: Purpose of randomization

37 ANS: B PTS: 1 TOP: 68-95-99.7 rule

38 ANS: F PTS: 1 TOP: Stratification and blocking

39 ANS: E PTS: 1 TOP: Units for numerical measures

40 ANS: K PTS: 1 TOP: Behavior of median

41 ANS: B PTS: 1 TOP: Interpret slope/computer output

42 ANS: J PTS: 1 TOP: Interpret s from computer output

43 ANS: B PTS: 1 TOP: Calculate residual

44 ANS: K PTS: 1 TOP: Extrapolation

45 ANS: E PTS: 1 TOP: Simulation to estimate probability

46 ANS: G PTS: 1 TOP: Identify experimental units

47 ANS: A PTS: 1 TOP: Scope of inference

48 ANS: K PTS: 1 TOP: Impact of transformation on numerical summaries

49 ANS: A PTS: 1 TOP: How r is calculated

50 ANS: H PTS: 1 TOP: Statistical significance

51 ANS: A PTS: 1 TOP: Mean of density curve

52 ANS: J PTS: 1 TOP: Interpret residuals

53 ANS: A PTS: 1 TOP: 68-95-99.7 rule

54 ANS: J PTS: 1 TOP: General addition rule (and multiplication of indep. events)

55 ANS: B PTS: 1 TOP: Stratified random sample

56 ANS: K PTS: 1 TOP: Normal Calculations

57 ANS: E PTS: 1 TOP: Conditional probability formula

58 ANS: J PTS: 1 TOP: Multiplication rule, dependent events

59 ANS: C PTS: 1 TOP: Standard deviation of Normal distribution from quartiles

60 ANS: G PTS: 1 TOP: Mean and standard deviation behavior

61 ANS: C PTS: 1 TOP: Identify sampling frame

62 ANS: F PTS: 1 TOP: Identify sample

63 ANS: C PTS: 1 TOP: Principles of experimental design

64 ANS: K PTS: 1 TOP: Mean and standard deviation of standard scores

65 ANS: D PTS: 1 TOP: Idea of random digits table

66 ANS: J PTS: 1

67 ANS: A PTS: 1 TOP: Idea of probability/Myths

68 ANS: J PTS: 1 TOP: What least-squares means

69 ANS: D PTS: 1 TOP: Conditional probability formula

70 ANS: F PTS: 1 TOP: Voluntary response

71 ANS: E PTS: 1 TOP: What a SRS doesn't do

72 ANS: H PTS: 1 TOP: Independent and mutually exclusive events

ID: A

3

73 ANS: B PTS: 1 TOP: Normal Calculations

74 ANS: F PTS: 1 TOP: Compare two categorical variables (not in two-way tablE.

75 ANS: E PTS: 1 TOP: Scatterplot basics

76 ANS: G PTS: 1 TOP: Choosing the right measures

77 ANS: B PTS: 1 TOP: Cumulative freq. graph

78 ANS: J PTS: 1 TOP: Interpret stem plot

79 ANS: A PTS: 1 TOP: Interpret stem plot

80 ANS: G PTS: 1 TOP: Interpret stem plot

81 ANS: C PTS: 1 TOP: Purpose of replication

82 ANS: J PTS: 1 TOP: Percentiles

83 ANS: B PTS: 1 TOP: Causation

84 ANS: F PTS: 1 TOP: Estimating r from scatter

85 ANS: C PTS: 1 TOP: Categorical vs Quantitative variables

86 ANS: H PTS: 1 TOP: Multiplication Rule, Independent events

87 ANS: C PTS: 1 TOP: Independent and mutually exclusive events

88 ANS: J PTS: 1 TOP: General addition rule (and multiplication of indep. events)

89 ANS: E PTS: 1 TOP: Characteristics of LSRL

90 ANS: H PTS: 1 TOP: Confounding

91 ANS: A PTS: 1

92 ANS: J PTS: 1 TOP: Interpret segmented bar graph

93 ANS: B PTS: 1 TOP: Negative association

94 ANS: J PTS: 1 TOP: Probability Myths

95 ANS: E PTS: 1 TOP: Interpreting correlation

96 ANS: F PTS: 1 TOP: Purpose of control

97 ANS: C PTS: 1 TOP: Definition of distribution

98 ANS: J PTS: 1

99 ANS: E PTS: 1 TOP: Recognizing Normal distribution

100 ANS: H PTS: 1 TOP: Normal Probability Plot

101 ANS: B PTS: 1 TOP: Estimating r from scatter

102 ANS: G PTS: 1 TOP: Z-score calculation

103 ANS: D PTS: 1 TOP: Independent and mutually exclusive events

104 ANS: H PTS: 1 TOP: When to use bar graphs and pie charts