AP Stats Unit 8

Which of these variables is binomial?

• time it takes to attempt 10 independent free throws

• time it takes to make 10 independent free throws

• number of shots made in 10 independent attempts at free throws

• number of attempts to make 10 independent free throws

• none of these

A college basketball player makes 80% of her free throws. Suppose this probability is the same for each free throw she attempts, and free throw attempts are independent. The expected number of free throws required until she makes her first free throw of the season is

• 2

• 1.25

• 0.80

• 0.31

• 0.13

Suppose that 40% of the cars in a certain town are white. A person stands at an intersection waiting for a white car. Let X = the number of cars that must drive by until a white one drives by. P(X < 5) =

• 0.0518

• 0.1296

• 0.2592

• 0.8704

• 0.9482

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 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

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

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

A recent survey of cell phone users indicated that 56 percent of the respondents prefer to use cell phones for texting rather than for making phone calls. A 95 percent confidence interval for the estimate of all cell phone users who prefer to use cell phones for texting has a margin of error of 3 percent. Assume all conditions for inference have been met. Based on the confidence interval, which of the following claims is supported?

• Less than half of all people prefer texting.

• More than half of all people prefer texting.

• At least 60 percent of all people prefer texting

• At least 75 percent of all people prefer texting.

Which of the following shows how to determine P(shaded number or number less than five)?

• 4/8 + 4/8 - 2/8

• 4/9 + 2/8 - 4/8

• 4/8 + 6/8 + 2/8

• 2/8 + 4/8 - 4/8