AP Stats - Unit 7 Review 2020

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

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

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 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)

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 iPad. 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 its 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.

A researcher initially plans to take an SRS of size 160 from a certain population and calculate the sample mean  $\overline{x}$  . Later, the researcher decides to increase the sample size so that the standard deviation of the sampling distribution of  $\overline{x}$  will be half as big as when using a sample size of 160. What sample size should the researcher use?

• 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 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 sampling 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 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 mean is distributed around the population mean

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

A newborn baby has extremely low birth weight (ELBW) if it weighs less than 1000 grams. A study of the health of such children in later years examined a random sample of 219 children. Their mean weight at birth was  $\overline{x}=810$  grams. This sample mean is an unbiased estimator of the mean weight  $\mu$  in the population of all ELBW babies, which means that 

• in all possible samples of size 219 from the population, the mean of the values of  $\overline{x}$  will equal 810.  

• in all possible samples of size 219 from this population, the mean of the values of  $\overline{x}$  will equal  $\mu$  

• as we take larger and larger samples from this population,  $\overline{x}$  will get closer and closer to  $\mu$   

• in all possible samples of size 219 form this population, the values of  $\overline{x}$  will have a distribution that is close to Normal. 

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

The magazine Sports Illustrated asked a random sample of 750 Division I college athletes, "Do you believe performance0enhancing drugs are a problem in college sports?" Suppose that 30% of all Division I athletes think that these drugs are a problem. Let p-hat be the sample proportion who say that these drugs are a problem. Which of the following are the mean and standard deviation of the sampling distribution of the sample proportion p-hat?

• Mean = 0.30, SD = 0.017

• Mean = 0.30, SD = 0.55

• Mean = 0.30, SD = 0.0003

• Mean = 225, SD = 12.5

• Mean = 225, SD = 157.5