AP Stats Unit 6

The manager of a city recreation center wants to estimate the percent of city residents who favor a proposal to build a new dog park. To gather data, the manager will select a random sample of city residents. Which of the following is the most appropriate interval for the manager to use for such an estimate?

• A one-sample z�-interval for a sample proportion

• A one-sample z�-interval for a population proportion

• A one-sample z�-interval for a difference between population proportions

• A two-sample z�-interval for a difference between population proportions

A random sample of 500 adults living in a large county was selected and 304 adults from the sample indicated that the unemployment rate was of great concern. What is the standard error of the sample proportion p^?

A town council wants to estimate the proportion of residents who are in favor of a proposal to upgrade the computers in the town library. A random sample of 100 residents was selected, and 97 of those selected indicated that they were in favor of the proposal. Is it appropriate to assume that the sampling distribution of the sample proportion is approximately normal?

• No, because the sample is not large enough to satisfy the normality conditions.

• No, because the size of the population is not known.

• Yes, because the sample was selected at random.

• Yes, because sampling distributions of proportions are modeled with a normal model

Sue and Javier are working on a statistics project to estimate the proportion of students at their school who have a pet dog. Sue selects a random sample of 81 students from the 2,400 students at their school, and Javier selects a separate random sample of 64 students. They will both construct a 90 percent confidence interval from their estimates. Consider the situation in which the sample proportion from Sue’s sample is equal to the sample proportion from Javier’s sample. Which of the following statements correctly describes their intervals?

• Javier’s interval will have a greater degree of confidence than Sue’s interval will.

• The width of Sue’s interval will be wider than the width of Javier’s interval.

• The width of Sue’s interval will be the same as the width of Javier’s interval.

• The width of Sue’s interval will be narrower than the width of Javier’s interval

Is this a probability distribution?

• No, the sum of p(x) does not equal 1.

• Yes, all p(x) are between 0 and 1.

• No, all p(x) are not between 0 and 1.

• Yes, the sum p(x) is 1.

• A

• B

• C

• D

• E

Is this a probability distribution?

• No

• Yes

Suppose a 90 percent confidence interval to estimate a population proportion was calculated from a sample proportion of 18 percent and a margin of error of 4 percent. What is the width of the confidence interval?

• 2 percent

• 4 percent

• 8 percent

• 16 percent

Suppose a researcher wants to use a confidence interval to estimate an unknown population proportion p�. Which of the following is not a correct statement?

• The endpoints of the interval can vary with each new sample.

• The probability that p� is in the interval is equal to the level of confidence for the interval.

• Whether the interval captures p� is not known with certainty

• The population proportion p� is fixed, but the sample proportion pˆ�^ can vary from sample to sample.

A recent national survey indicated that 73 percent of respondents try to include locally grown foods in their diets. A 95 percent confidence interval for the proportion of all people in the country who try to include locally grown foods in their diets is given as (0.70,0.76)(0.70,0.76). Assume all conditions for inference were met. Based on the confidence interval, which of the following claims is supported?

• Less than half of all people in the country try to include locally grown foods in their diets.

• Less than half of all people in the country try to include locally grown foods in their diets.

• Less than 80 percent of all people in the country try to include locally grown foods in their diets

• Less than 75 percent of all people in the country try to include locally grown foods in their diets