AP Stats Ch7 MC Review

A study of voting chose 663 registered voters at random shortly

after an election. Of these, 72% said they had voted in the election.

Election records show that only 56% of registered voters voted in

the election. Which of the following statements is true?

• 72% is a sample; 56% is a population.

• 72% and 56% are both statistics.

• 72% is a statistic and 56% is a parameter.

• 72% is a parameter and 56% is a statistic.

• 72% and 56% are both parameters.

Tags

CCSS.HSS.IC.B.3

Fill in the blank: The _ says that when n is large, the sampling distribution of the sample mean x̄ is approximately Normal.

• unbiased estimator

• sampling distribution of the sample proportion

• sampling distribution of the sample mean

• Central Limit Theorem

Tags

CCSS.6.SP.A.3

The Gallup Poll has decided to increase the size of its random

sample of voters from about 1500 people to about 4000 people

right before an election. The poll is designed to estimate the

proportion of voters who favor a new law banning smoking in

public buildings. The effect of this increase is to

• reduce the bias of the estimate.

• increase the bias of the estimate.

• reduce the variability of the estimate.

• increase the variability of the estimate.

• reduce the bias and variability of the estimate.

Why is it important to check the 10% condition before calculating

probabilities involving x̄?

• To reduce the variability of the sampling distribution of x̄

• To ensure that the distribution of x̄ is approximately Normal

• To ensure that we can generalize the results to a larger population

• To ensure that x̄ will be an unbiased estimator of μ

• To ensure that the observations in the sample are close to

  independent

Fill in the blank: A statistic used to estimate a parameter is an _ if the mean of its sampling distribution is equal to the value of the parameter being estimated.

• unbiased estimator

• sampling distribution of the sample proportion

• sampling distribution of the sample mean

• Central Limit Theorem

The central limit theorem is important in statistics because it

allows us to use a Normal distribution to find probabilities

involving the sample mean if the

• sample size is reasonably large (for any population).

• population is Normally distributed (for any sample size).

• population is Normally distributed and the sample size is

  reasonably large.

• population is Normally distributed and the population standard

  deviation is known (for any sample size).

• population size is reasonably large (whether the population

  distribution is known or not).

Tags

CCSS.HSS.ID.A.4

The number of undergraduates at Johns Hopkins University is

approximately 2000, while the number at Ohio State University is

approximately 60,000. At both schools, a simple random sample of

about 3% of the undergraduates is taken. Each sample is used to

estimate the proportion p of all students at that university who own

an iPod. Suppose that, in fact, p = 0.80 at both schools. Which of

the following is the best conclusion?

• We expect that the estimate from Johns Hopkins will be closer

  to the truth than the estimate from Ohio State because it comes

  from a smaller population.

• We expect that the estimate from Johns Hopkins will be closer

  to the truth than the estimate from Ohio State because it is

  based on a smaller sample size.

• We expect that the estimate from Ohio State will be closer to

  the truth than the estimate from Johns Hopkins because it

  comes from a larger population.

• We expect that the estimate from Ohio State will be closer to

  the truth than the estimate from Johns Hopkins because it is

  based on a larger sample size.

• We expect that the estimate from Johns Hopkins will be about

  the same distance from the truth as the estimate from Ohio

  State because both samples are 3% of their populations.

Fill in the blank: The _ p̂ describes the distribution of values taken by the sample proportion p̂ in all possible samples of the same size from the same population.

• unbiased estimator

• sampling distribution of the sample proportion

• sampling distribution of the sample mean

• Central Limit Theorem

The student newspaper at a large university asks an SRS of 250

undergraduates, “Do you favor eliminating the carnival from the

term-end celebration?” All in all, 150 of the 250 are in favor.

Suppose that (unknown to you) 55% of all undergraduates favor

eliminating the carnival. If you took a very large number of SRSs

of size n=250 from this population, the sampling

distribution of the sample proportion p̂ would be

• exactly Normal with mean 0.55 and standard deviation 0.03.

• approximately Normal with mean 0.55 and standard deviation

  0.03.

• exactly Normal with mean 0.60 and standard deviation 0.03.

• approximately Normal with mean 0.60 and standard deviation

  0.03.

• heavily skewed with mean 0.55 and standard deviation 0.03.

Which of the following statements about the sampling distribution

of the sample mean is incorrect?

• The standard deviation of the sampling distribution will

  decrease as the sample size increases.

• The standard deviation of the sampling distribution measures

  how far the sample mean typically varies from the population

  mean.

• The sample mean is an unbiased estimator of the population

  mean.

• The sampling distribution shows how the sample is distributed

  around the sample mean.