AP Statistics

Chapter 7 Test Review Answers

Concept Question #1

• A survey conducted by an unnamed polling firm stated on October 29th, that Barack Obama was predicted to receive 49.8% of the vote on election day. On the actual day of the election, he received 50.97% of the vote. – Part a: Which of these numbers is a statistic?

• ANS: 49.8%

– Part b: Which of these number is a parameter?• ANS: 50.97%

– Part c: after answering part a & b above, write each of the given numbers using the correct ‘symbol’. • ANS: p = .5097 & = .498

Concept Question #2

• When we talk about the ‘variability’ of a statistic, then we are focusing on what aspect of a distribution?– ANSWER: The spread of the distribution.

Concept Question #3

• When we talk about the amount of “bias” in a statistic, then what aspect of the distribution are we talking about?– ANSWER: The center of the distribution

Concept Question #4

• MULTIPLE CHOICE: Which of the following is the preferred characteristic of an estimate of a parameter– A. A statistic with high variability and low bias– B. A statistic with high variability and high bias– C. A statistic with low variability and low bias– D. A statistic with low variability and high bias– E. It doesn’t matter how much bias or variability a

statistic contains• ANSWER: C…. The less bias and variability… the better.

Concept Question #5

• If you wish to reduce the amount of variability in a statistic that we hope to use to estimate a parameter, then what is the best way to accomplish this?– ANSWER: INCREASE the sample size.

Concept Question #6

• Two polling companies come to Pulaski County (pop. 65,000) with the hopes of completing a survey of its residents. One company plans to survey 2500 residents, and the other plans to survey 3100 residents. Which of the sampling distributions would have the smaller ?– ANSWER: The survey with 3100 residents… the

larger sample size, DECREASES variability/spread, so it would produce a SMALLER standard deviation (

Concept Question #7

• A survey in 2006 of 500 randomly selected Kentuckians found that 74% of them rooted for the Wildcats, 21% of them supported the Cards, and 5% of them supported neither. Suppose that the actual percentage of Wildcat supporters was 63%. – Part a: The mean of of p would be?

• ANSWER: … recall that we always use the ‘actual’ value for this mean.

– Part b: Is 63% a parameter or a statistic?• ANSWER: parameter

– Part c: Which of the following numbers is unknown: 74% or 63%?• ANSWER: Technically, only God knows the value of a parameter, so

63% is unknown.

Concept Question #8

• A survey in 2006 of 500 randomly selected Kentuckians found that 74% of them rooted for the Wildcats, 21% of them supported the Cards, and 5% of them supported neither. Suppose that the actual percentage of Wildcat supporters was 63%. – Part a: What would the standard deviation ( be?

• ANSWER:

– Part b: What condition must be met in order to complete the calculation stated in part a? • ANSWER: the 10% condition, which states “the population MUST

be at least 10 times greater than the sample” • This is often written symbolically as: n ≤ 0.10 N or n ≤

Concept Question #9

• A member of our boy’s basketball team makes 70% of his free throw shots. Due to the fact that this player is a starter and will play many minutes in each game, he will make exactly 100 free throw attempts by season’s end. Assuming that each free throw is independent, what is the probability that his number of made free throws exceeds 70?– ANSWER: 0.500

• WORK SHOWN BELOW: – 70 out of 100 is .70 (70%)– P(z > ) = P(z > 0), which is 0.500

Concept Question #10

• Part a: In simplistic language, state the main idea of the Central Limit Theorem.– As ‘n’ increases, the sampling distribution

becomes more ‘normal’ in nature.• Part b: In simplistic language, state the main

idea of the Law of Large Numbers. – As ‘n’ increases, the value of gets closer and

closer to the value of .

Concept Question #11

• What is the ‘magic number’ that ensures that a sampling distribution (FOR MEANS) will be approximately normal, even if the parent population is highly skewed to the right?– ANSWER: According to the Central Limit

Theorem, 30 is the ‘magic number’. – Note: DO NOT use the phrase ‘magic number’ in

your answer to a FRQ on a test or on the AP EXAM…

Concept Question #12

• What EXACTLY is the condition (FOR PROPORTIONS) that must be met in order to conclude that a ‘normal approximation’ can be made (i.e.: distribution is normal)?

–ANSWER: n·p ≥ 10 AND n·q ≥ 10

Concept Question #13

• What is the formula for standardizing (find a z-score) for a proportion?

Z =

Concept Question #14

• What is the formula for standardizing (find a z-score) for a sample mean?

Z =

Concept Question #15

• If we take many simple random samples (SRS’s) from the exact same population what do we expect to have happen?

• ANSWER: The values of the statistics that we get from that population will vary from sample to sample.

Concept Question #16• The chipmunk population in a certain area is known to have a mean weight of 84

grams and a standard deviation of 18 grams. A wildlife biologist weighs 9 chipmunks that have been caught in live traps before releasing them. Which of the following best describes what we know about the sampling distribution of means for the biologist’s sample?

• NOTE: there was no mention of the word proportion on this problem for good reason.. It has nothing to do with a proportion, but everything to do with a mean…

• ANSWER: • Center: • Spread: (NOTE: We are allowed to make this calculation, because it is VERY safe

to say that the population of chipmunks is almost certainly greater than 10 times 9 (which would be 90 total chipmunks).

• SHAPE: Since the ‘n’ is rather small (n is only 9), then we CANNOT assume normality, so the shape of the distribution is unknown and cannot be assumed to be approximately normal. ‘n’ would have needed to be greater than 30 for us to assume normality in this situation.

Concept Question #17

• Which of the following best describes a sampling distribution?• A. The distribution of all values of a statistic found in a large

number of simulated samples of size n.• B. The set of all values of a variable in a sample of size n.• C. The set of all values of a variable in a large number of

samples of size n.• D. The distribution of parameter values in all possible

samples of size n.• E. A probability distribution that describes the relative

likelihood of all possible values of a statistic.• Answer: E

Concept Question #18• In a large population of adults, the mean IQ is 112 with a

standard deviation of 20. Suppose 200 adults are randomly selected for a market research campaign. The sampling distribution of the sample mean IQ is

• A. exactly Normal, mean 112, standard deviation 20.• B. approximately Normal, mean 112, standard deviation 0.1.

• C. approximately Normal, mean 112, standard deviation 1.414.

• D. approximately Normal, mean 112, standard deviation 20.

• E. exactly Normal, mean 112, standard deviation 1.414.• ANSWER: C

Concept Question #19• Suppose you are sampling from a distribution that is strongly skewed left.

Which of the following statements about the sampling distribution of the sample mean is true?

• A. As the sample size increases, the shape of the sampling distribution gets closer and closer to a Normal distribution.

• B. As the sample size increases, the shape of the sampling distribution gets closer and closer to the shape of the population distribution.

• C. As the sample size increases, the mean of the sampling distribution gets closer to the population mean.

• D. Regardless of the sample size, the shape of the sampling distribution is similar to the shape of the population distribution.

• E. Regardless of the sample size, the standard deviation of the sampling distribution is approximately equal to the standard deviation of the population.

• ANSWER: A

Concept Question #20• Suppose we wish to estimate the percentage of students who smoke

cigarettes at each of several colleges and universities. Two of the colleges are Wabash College (enrollment 900) and Purdue University (enrollment 36,000). What should the relative size of our samples be from each school if we want the two sampling distributions to have approximately the same standard deviation?

• A. Because the population sizes are so different, it’s impossible to make the standard deviations equal by adjusting the two sample sizes.

• B. We should take a larger number of Purdue students, since there are more of them.

• C. We should take a larger number of Wabash students, since there are fewer of them.

• D. We should take the same size samples from each school.• E. We should take samples that are exactly 10% of each school’s

enrollment.• ANSWER: D

Concept Question #21• A statistic is said to be unbiased if• A. the survey used to obtain the statistic was designed so as

to avoid even the hint of racial or sexual prejudice.• B. the mean of its sampling distribution is equal to the true

value of the parameter being estimated.• C. both the person who calculated the statistic and the

subjects whose responses make up the statistic were truthful.

• D. the value from any sample is equal to the parameter being estimated.

• E. it is used for honest purposes only.• ANSWER: B