Name__________________________________________ AP Statistics Fall 2015 Final REVIEW

Chapter 1: Exploring Data Creating & interpreting Boxplots Choosing the appropriate type of graph for data (categorical vs. quantitative) Describing distributions (SCS-GO) Cumulative relative frequency graphs

Use the following scenario for questions 1 – 3. For 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.

_______ 1. The median point total for this class is a. 130 b. 130.5 c. 133 d. 134.4 e. 137

_______ 2. This stemplot is most similar to a. 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.

_______ 3. To which of the following data sets does this stemplot corresponds? a. All integers between 116 and 179. b. 1, 2, 3, 4, 6, 6, 7, 8, 8, 9c. 16, 18, 21, 24, 28, 33, 37, 42, 46, 79d. 116, 118, 121, 124, 128, 133, 137, 142, 146, 179e. None of these.

Use the following scenario for questions 4 – 6. The following is a boxplot of the birth weights (in ounces) of a sample of 160 infants in a local hospital.

_______ 4. The number of children with birth weights between 102 and 122 ounces is around: a. 20.b. 40.c. 50.d. 80.e. 100.

11 6 812 1 4 813 3 714 2 6151617 9

_______ 5. The median birth weight is approximatelya. 80.5 ounces. d. 110 ounces. b. 90 ounces. e. 120 ounces. c. 100 ounces.

_______ 6. About 40 of the birth weights were below: a. 92 ounces. d. 122 ounces. b. 102 ounces. e. 132 ounces. c. 112 ounces.

_______ 7. An ecologist studying Pisaster starfish was interested in the distribution of sizes of starfish on a certain shoreline. One measure of size is “arm length.” Shown is the cumulative relative frequency distribution for the arm length of 102 Pisaster individuals.

The median and interquartile range of this distribution are approximately: a. Median is 15.2 and Interquartile range is 12.5 to 16.2. b. Median is 13 and Interquartile range is 13 to 16.1.c. Median is 13 and Interquartile range is 3.1.d. Median is 13 and Interquartile range is 3.7.e. Median is 15.2 and Interquartile range is 3.7.

Use the following scenario for question 8 and 9. A sample was taken of the salaries of 20 employees of a large company. The following boxplot shows the salaries (in thousands of dollars) for this year.

_______ 8. Based on the boxplot, which of the following statements is true? a. The maximum salary is between $60,000 and $70,000. b. The minimum salary is $20,000. c. The range of the middle half of the salaries is about $20,000. d. The median salary is about $40,000. e. 25% of the employees make more than $70,000.

_______ 9. Based on the boxplot, the five-number summary is a. 28, 39, 48, 60.5, 77b. 28, 41, 48, 58, 77c. 28, 39, 51, 58, 77d. 28, 41, 51, 60.5, 77e. 26, 39, 48, 60.5, 81

_______ 10. 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%

_______ 11. The histogram below shows the length (in minutes) of 140 songs by the band Wilco.

Which of the following descriptions best fits this distribution? a. Skewed right, centered at about 8, with several high outliers.b. Skewed left, centered at about 8, with several high outliers. c. Skewed right, centered at about 4.5, with several high outliers. d. Skewed left, centered at about 4.5, with several high outliers. e. Skewed left, centered at about 3.5, with several high outliers.

_______ 12. The table shows the results of the New Hampshire Republican Presidential Primary on January 10, 2012.

Which of the following lists of graphs are all appropriate ways of presenting these data?

a. Bar graph, Pie chart, Boxplotb. Bar graph, Boxplotc. Bar graph, Pie chartd. Bar graph onlye. Pie chart only

Candidate Percentage of votes

Mitt Romney 39Ron Paul 23

John Huntsman 17Rick Santorum 9Newt Gingrich 9

Other 3

Chapter 2: Modeling Distributions of Data Calculating z-scores using formula Using z-scores to compare Normal distributions calculations Transformations to z-scores and numerical statistics (mean, st. dev., etc.)

_______ 13. If 30 is added to every number on a list, which of the following does not change? a. the mean. d. the median. b. the mode. e. the standard deviation. c. the 75th percentile.

Use the following scenario for questions 14 and 15. A sample was taken of the salaries of 20 employees of a large company. The following are the salaries (in thousands of dollars) for this year. For convenience, the data are ordered.

28 31 34 35 37 41 42 42 42 4749 51 52 52 60 61 67 72 75 77

Suppose each employee in the company receives a $3,000 raise for next year (each employee’s salary is increased by $3,000).

_______ 14. The mean salary for the employees will a. be unchanged. d. increase by √$ 3,000 .b. increase by $3,000. e. increase by $150. c. be multiplied by $3,000.

_______ 15. The z-scores of the salaries for the employees will a. be unchanged. d. increase by √$ 3,000 .b. increase by $3,000. e. decrease by $3,000. c. be multiplied by $3,000.

_______ 16. Ramon is planning on buying a new car. He’s looking at the Ford Escape—a SUV—which gets 28 highway miles per gallon, and the Ford Fusion—a mid-sized sedan—which gets 31 highway miles per gallon. The mean fuel efficiency for all SUVs is 23, with a standard deviation of 7.6. The mean of all mid-sized sedans is 27, with a standard deviation of 5.2 Which vehicle has a better standing, relative to others of the same style? a. The Ford Fusion sedan has a better relative standing, because it’s z-score is higher. b. The Ford Fusion sedan has a better relative standing, because it’s z-score is closer to 0. c. The Ford Escape SUV has a better relative standing, because it’s z-score is higher.d. The Ford Escape SUV has a better relative standing, because it’s z-score is closer to 0. e. We can’t make any comparisons unless we know that the distributions of fuel efficiency for vehicle types is Normally distributed.

_______ 17. The distribution of household incomes in a small town is strongly skewed to the right. The mean income is $42,000 and the standard deviation is $24,000. The Ames family’s household income is $60,000. The z-score for the Ames family’s income is a. - 0.75 d. 0.86b. 0.3 e. None of these, because z-score cannot bec. 0.75 used unless the distribution is Normal.

_______ 18. If the values in a data set are in feet, then what are the units for standard scores?

a. Feet d. 1Feet

b. Square feet e. Standard scores do not have unitsc. Square root of feet.

_______ 19. Jack and Jill are both enthusiastic players of a certain computer game. Over the past year, Jack’s mean score when playing the game is 12,400 with a standard deviation of 1500. During the same period, Jill’s mean score is 14,200 with a standard deviation of 2000. They devise a fair contest: each one will play the game once, and they will compare z-scores. Jack gets a score of 14,000, and Jill gets a score of 16,000. Who won the contest, and what were each of their z-scores? a. Jack’s z=1.07; Jill’s z=1.11; Jill wins the contest. b. Jack’s z=1.07; Jill’s z=0.90; Jack wins the contest.c. Jack’s z=0.94; Jill’s z=1.11; Jill wins the contest. d. Jack’s z=0.94; Jill’s z=0.90; Jack wins the contest.e. Jack’s z=0.81; Jill’s z=0.99; Jill wins the contest.

_______ 20. Using the standard Normal distribution tables, the area under the standard Normal curve corresponding to −0.5<Z<1.2 is a. 0.2815. d. 0.5764.b. 0.3085. e. 0.8849. c. 0.3661.

Chapter 3: Describing Relationships (Scatterplots) Characteristics of Least-Squares Regression lines (LSRL) Creating LSRL from summary statistics (with formulas) Calculate residuals Characteristics of correlation, r Interpreting slope of LSRL Interpreting r2 Interpreting computer output for LSRL, s, r2, etc. Residual plots (look for any leftover pattern to determine if the model is appropriate) Extrapolation

Use the following scenario for questions 21 and 22. Below is a scatterplot (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 also shown.

Predictor Coef SE Coef T PConstant 2.08 15.93 0.13 0.899Calories 0.06297 0.02409 2.61 0.028

S = 3.37648 R-Sq = 43.2% R-Sq(adj) = 36.9%

_______ 21. Which of the following statements is a correct interpretation of the slope of the regression line? a. For each 1-unit increase in calories, the predicted protein increases by 2.08 grams. b. For each 1-unit increase in calories, the predicted protein increases by 0.063 grams.c. For each 1-gram increase in protein, the predicted calories increases by 2.08 grams.d. For each 1-gram increase in protein, the predicted calories increases by 0.063 grams.e. For each 1-gram increase in protein, the predicted calories increases by 0.024 grams.

_______ 22. The circled point on the scatterplot represents lima beans, which have 621 calories and 37 grams of protein. The residual for lima beans is: a. -37.0 d. 37.0b. -4.18 e. 41.18c. 4.18

_______ 23. The fraction of the variation in the values of a response y that is explained by the least-squares regression of y on x is the a. correlation coefficient.b. slope of the least-squares regression line. c. square of the correlation coefficient. d. intercept of the least-squares regression line. e. sum of the squared residuals.

_______ 24. Scores on the 1995 SAT verbal aptitude test x among Kentucky high school seniors were normally distributed with mean 420 and standard deviation 80. Scores on the 1995 SAT math aptitude test y among Kentucky high school seniors were normally distributed with mean 440 and standard deviation 60. The least-squares regression line has the equation y=188+0.6 x. The correlation between verbal scores and math scores is a. -0.8 d. 0.8b. 0 e. cannot be determined from the c. 0.45 information given

Use the following scenario for questions 25 and 26. A fisheries biologist studying whitefish in a Canadian Lake collected data on the length (in cm) and egg production for 25 female fish. A scatterplot of her results and computer regression analysis of egg productions 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 0.15 0.888Length 39.25 5.392 2.51 0.014

S = 2.1346 R-Sq = 67.2% R-Sq(adj) = 69.2%

_______ 25. The equation of the least-squares regression line is a. Eggs=−142.74+39.25 (Length)b. Eggs=39.25−142.74 (Length)c. Eggs=25.55+5.392(Length)d. Length=25.55+5.392(Eggs)e. Length=−142.74+39.25 (Eggs)

_______ 26. Which of the following is the plot of residuals versus fish lengths? a. d.

b. e.

c.

Use the following scenario for questions 27 and 28. The 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.

Alcohol Heart disease Alcohol Heart diseaseCountry from wine Deaths Country from wine DeathsAustralia 2.5 211 Netherlands 1.8 167Austria 3.9 167 New Zealand 1.9 266Belgium 2.9 131 Norway 0.8 227 Canada 2.4 191 Spain 6.5 86Denmark 2.9 220 Sweden 1.6 207Finland 0.8 297 Switzerland 5.8 115France 9.1 71 United Kingdom 1.3 285Iceland 0.8 211 United States 1.2 199Ireland 0.7 300 West Germany 2.7 172Italy 7.9 107

_______ 27. If heart disease death rate were expressed as deaths per 1,000 instead of as deaths per 100,000 people, how would the correlation r between wine consumption and heart disease death rate change? a. r would be divided by 100. d. r would be multiplied by 10.b. r would be divided by 10. e. r would be multiplied by 100.c. r would not change.

_______ 28. Do these data provide strong evidence that drinking wine actually causes a reduction in heart disease deaths? 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.

_______ 29. Suppose a straight line is fit to data having response variable y and explanatory variable x. Predicting values of y for values of x outside the range of the observed data is a. contingency . d. correlation. b. extrapolation. e. interpolation. c. causation.

_______ 30. The correlation between the age and height of children is found to be about r=0.7. Suppose we use the age x of a child to predict the height y of the child. We conclude that

a. the least-squares regression line of y on x would have a slope of 0.7. b. the proportion of the variation in heights explained by the least-squares regression line of y on x is 0.49. c. about 70% of the time, age will accurately predict height. d. the proportion of the variation in heights explained by the least-squares regression line of y on x is 0.70. e. the line explains about 49% of the data.

_______ 31. Consider the following scatterplot of two variables, X and Y.

We may conclude that the correlation between X and Y a. must be close to -1, since the relationship between X and Y is clearly non-linear. b. must be close to 0, since the relationship between X and Y is clearly non-linear. c. is close to 1, even though the relationship is not linear. d. may be exactly 1, since the points lie on the same curve. e. greater than 1, since the relationship is non-linear.

_______ 32. Which of the following are most likely to be negatively correlated? a. The total floor space and the price of an apartment in New York. b. The percentage of body fat and the time it takes to run a mile for male college students. c. The heights and yearly earnings of 35-year-old U.S. adults.d. Gender and yearly earnings among 35-year-old U.S. adults. e. The prices and the weights of all racing bicycles sold last year in Chicago.

Chapter 4: Designing Studies Observational Study vs. Experiments 4 principles of Experimental design (Comparison, Randomization, Control, Replication) Definitions/differences between SRS, stratified random sample, cluster sample, etc.

_______ 33. The principle reason for the use of random assignment in designing experiments is that it a. 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.

_______ 34. 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.

_______ 35. The most important advantage of experiments over observational studies is thata. experiments are usually easier to carry out. b. experiments can give better evidence of causation. c. confounding cannot happen in experimentsd. an observational study cannot have a response variable. e. observational studies cannot use random samples.

_______ 36. A stratified random sample is appropriate when a. it is impractical to take a simple random because the population is too large. b. the population can be easily subdivided into groups according to some categorical variable, and the variable you are measuring is quite different within the groups but very similar between groups. c. the population can be easily subdivided into groups according to some categorical variable, and the variable you are measuring is very similar within the groups but quite different between groups. d. you intend to take a sample of more than 100 individuals. e. you want to avoid undercoverage of certain groups.

Use the following scenario for questions 37 and 38. In 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.

_______ 37. 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.

_______ 38. Which of the following best describes the inferences the researcher can make based on his results? a. He can make inferences about cause and effect, but not about the populations from which the samples were taken. b. He can make inferences about the population from which the samples were taken, but not about cause and effect. c. He can make inferences about both cause and effect and the population from which the samples were taken. d. He cannot make inferences about either cause and effect or the population from which the samples were taken. e. There is not enough information to make judgements about the scope of inference.

_______ 39. We 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 given.

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 from left to right, starting at the beginning of the list.

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

The simple random sample isa. 117. b. Bechhofer, Bechhofer again, and Taylor. c. Bechhofer, Taylor, Weiss. d. Kesten, Kiefer, Taylor. e. Taylor, Weiss, Ito.

Chapter 5: Probability Number assignment for simulations Probability rules Probabilities from a two-way table/tree diagram Mutually exclusive vs. independence (be able to prove two events are/are not independent)

_______ 40. Students at University X must have one of four class ranks—freshman, sophomore, junior, or senior. At University X, 35% of the students are freshmen and 30% are sophomores. If a University X student is selected at random, the probability that he/she is either a junior or a senior isa. 30% b. 35% c. 65% d. 70% e. 89.5%

_______ 41. A box has 10 tickets in it, two of which are winning tickets. You draw a ticket at random. If it's a winning ticket, you win. If not, you get another chance, as follows: your losing ticket is replaced in the box by a winning ticket (so now there are 10 tickets, as before, but 3 of them are winning tickets). You get to draw again, at random. Which of the following are legitimate methods for using simulation to estimate the probability of winning?I. Choose, at random, a two-digit number. If the first digit is 0 or 1, you win on the first draw; If the first digit is 2 through 9, but the second digit is 0, 1, or 2, you win on the second draw. Any other two-digit number means you lose.II. Choose, at random, a one-digit number. If it is 0 or 1, you win. If it is 2 through 9, pick a second number. If the second number is 8, 9, or 0, you win. Otherwise, you lose.III. Choose, at random, a one-digit number. If it is 0 or 1, you win on the first draw. If it is 2, 3, or 4, you win on the second draw; If it is 5 through 9, you lose.

a. I only d. I and IIb. II only e. I, II, and IIIc. III only

_______ 42. You want to use simulation to estimate the probability of getting exactly one head and one tail in two tosses of a fair coin. You assign the digits 0, 1, 2, 3, 4 to heads and 5, 6, 7, 8, 9 to tails. Using the following random digits to execute as many simulations as possible, what is your estimate of the probability?

19226 95034 05756 07118

a. 1/20 b. 1.10 c. 5/10 d. 6/10 e. 2/3

_______ 43. Event A has probability 0.4. Event B has probability 0.5. If A and B are independent, then the probability that both events occur is

a. 0.0. b. 0.1. c. 0.2. d. 0.7. e. 0.9.

_______ 44. Suppose that A and B are independent events with P (A )=0.2 and P (B )=0.4. What is P(A∪B)?

a. 0.08 b. 0.12 c. 0.44 d. 0.52 e. 0.60

_______ 45. A 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 = Student ate breakfast that morning.N = Student didn’t eat breakfast that morning.

What is the probability that the selected student is a male and ate breakfast?

a. 0.32 d. 0.64b. 0.40 e. 0.80c. 0.50

_______ 46. 100 high school students were asked if they had a dog, a cat, or both at home.

Dog? TotalNo Yes

Cat? No 74 4 78Yes 10 12 22Total 84 16 100

If a single student is selected at random and you know she has a dog, what is the probability she also has a cat? a. 0.04 b. 0.12 c. 0.22 d. 0.25 e. 0.75

_______ 47. The 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.

If a randomly selected person is tested and the result is positive, the probability the individual has the disease is

a. 0.001. b. 0.019. c. 0.020. d. 0.021 e. 0.047

_______ 48. Suppose 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.

The events A and B area. disjoint.b. conditional.c. independent.d. reciprocals. e. complementary.

Use the following scenario for questions 49 and 50. You ask a sample of 370 people, “Should clinical trials on issues such as heart attacks that affect both sexes use subjects of just one sex?” The responses are in the table below.

Suppose you choose one of these people at random.

_______ 49. What is the probability that the person is a woman, given that she said “Yes?”a. 0.20b. 0.22c. 0.25d. 0.50e. 0.575

_______ 50. What is the probability that the person said “Yes,” given that she is a woman? a. 0.20b. 0.22c. 0.25d. 0.50e. 0.575

Yes NoMale 34 105

Female 46 185