AP Statistics Unit 5 Progress Check: MCQ Part B

In a certain region of the country, the proportion of the population with blue eyes is currently 17 percent. A random sample of 100 people will be selected from the population. What is the mean of the sampling distribution of the sample proportion of people with blue eyes for samples of size 100 ?

0.17

A sample of manufactured items will be selected from a large population in which 8 percent of the items are defective. Of the following, which is the least value for a sample size that will allow for the sampling distribution of the sample proportion to be assumed approximately normal?

125

For a certain population of men, 8 percent carry a certain genetic trait. For a certain population of women, 0.5 percent carry the same genetic trait. Let pˆ1 represent the sample proportion of randomly selected men from the population who carry the trait, and let pˆ2p^2 represent the sample proportion of women from the population who carry the trait. For which of the following sample sizes will the sampling distribution of pˆ1−pˆ2 be approximately normal?

200 men and 2,000 women

At a national convention attended by many educators, about 30 percent of the attendees are from the northeast. Of all the attendees of the national convention, 25 will be selected at random to receive a free book. What are the mean and standard deviation of the sampling distribution of the proportion of attendees from the northeast for samples of size 25 ?

C The mean is 0.3 and the standard deviation is √0.3(0.7)/25.

A study reported that finger rings increase the growth of bacteria on health-care workers' hands. Research suggests that 31 percent of health-care workers who wear rings have bacteria on one or both hands, and 27 percent of health-care workers without rings have bacteria on one or both hands. Suppose that independent random samples of 100 health-care workers wearing rings and 100 health-care workers not wearing rings are selected. What is the standard deviation of the sampling distribution of the difference in the sample proportions (wear rings minus does not wear rings) of health-care workers having bacteria on one or both hands?

C √0.31(0.69)100+0.27(0.73)100

For two populations of rabbits, R and S, the proportions of rabbits with white markings on their fur are given as pR and pS, respectively. Suppose that independent random samples of 50 rabbits from R and 100 rabbits from S are selected. Let pˆR be the sample proportion of rabbits with white markings from R, and let pˆS be the sample proportion of rabbits with white markings from S. What is the standard deviation of the sampling distribution of pˆR−pˆS ?

D √pR(1−pR)50+pS(1−pS)100

Researchers in plant growth are investigating the proportions of seedlings that sprout under two environmental settings in a lab experiment. Let pˆC represent the sample proportion of seedlings that sprout in garden C, and let pˆH represent the sample proportion of seedlings that sprout in garden H. For random samples of 100 garden C seedlings and 100 garden H seedlings, the sampling distribution of the difference between sample proportions pˆC−pˆH has σpˆC−pˆH≈0.051. Which of the following is the best interpretation of σPˆC−PˆH≈0.051 ?

E For all random samples of 100 garden C seedlings and 100 garden H seedlings, the average distance of all possible differences between sample proportions pˆC−pˆH from the mean of the sampling distribution is approximately 0.051.

A manufacturer of computer monitors estimates that 4 percent of all the monitors manufactured have a screen defect. Let pd represent the population proportion of all monitors manufactured that have a screen defect. For the sampling distribution of the sample proportion for samples of size 100, μPˆd=0.04. Which of the following is the best interpretation of μPˆd=0.04 ?

For all samples of size 100, the mean of all possible sample proportions of monitors manufactured that have a screen defect is 0.04.

A survey of 100 randomly selected dentists in the state of Ohio results in 78% who would recommend the use of a certain toothpaste. The population proportion is known to be p=0.72. For samples of size 100, which of the following best interprets the mean of the sampling distribution of sample proportion of dentists in the state of Ohio who would recommend the use of a certain toothpaste?

The mean of all sample proportions from all random samples of 100 dentists in the state of Ohio is equal to 0.72.

In one city, 75 percent of residents report that they regularly recycle. In a second city, 90 percent of residents report that they regularly recycle. Simple random samples of 75 residents are selected from each city. Which of the following statements is correct about the approximate normality of the sampling distribution of the difference in sample proportions of residents who report that they regularly recycle?

The sampling distribution is not approximately normal because although the sample size for the first city is large enough, the sample size for the second city is not large enough.

According to a recent survey, 47.9 percent of housing units in a large city are rentals. A sample of 210 housing units will be randomly selected. Which of the following must be true for the sampling distribution of the sample proportion of housing units in the large city that are rentals to be approximately normal?

The values of 210(0.479) and 210(0.521) must be at least 10.