Sampling Distributions AP Practice Test

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, 56% is a parameter

• 72% is a parameter, 56% is a statistic

• 72% and 56% are both parameters

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

1.   Suppose we select an SRS of size n = 100 from a large population having proportion p of successes.  Let p-hat be the proportion of successes in the sample.  For which value of p would it be safe to use the Normal approximation to the sampling distribution of  p-hat?

• 0.01

• 0.09

• 0.85

• 0.975

• 0.999

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 sufficiently 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 in reasonably large (whether the population distribution is known or not)

The number of undergraduates at Johns Hopkins University is approximately 2000, when the number at Ohio State University is approximately 60,000.  At both schools, a simple random sample of 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.  Supposed 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 population

• 40

• 80

• 320

• 640

• There is not enough information to determine the sample size

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  p-hat 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 sample 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 mean is distributed around the population mean

• The sampling distribution shows how the sample is distributed around the sample mean

• the person measuring the children’s weights does so without any error

• Normal

• approximately Normal

• right-skewed

• left-skewed

• symmetric, but not Normal