Unit 6 Progress Check: MCQ Part A (AP STATS)

Alma is estimating the proportion of students in her school district who, in the past month, read at least 1 book. From a random sample of 50 students, she found that 32 students read at least 1 book last month. Assuming all conditions for inference are met, which of the following defines a 90 percent confidence interval for the proportion of all students in her district who read at least 1 book last month?

0.64 +- 1.645 (square root( (0.64)(0.36)/50

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?

8 percent

Biologists studying horseshoe crabs want to estimate the percent of crabs in a certain area that are longer than 35 centimeters. The biologists will select a random sample of crabs to measure. Which of the following is the most appropriate method to use for such an estimate?

A one sample z-interval for a population proportion

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 population proportion

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). Assume all conditions for inference were met. Based on the confidence interval, which of the following claims is supported?

Less than 80 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?

More than half of all people prefer texting

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.

A marketing representative wants to estimate the proportion of people in a state who like the new design on the packaging of a certain cleaning product. The representative interviewed 100 people at a certain supermarket, and 82 people indicated that they liked the new design. Have the conditions for creating a confidence interval for the population proportion been met?

No, because the sample may not be representative of all people in the state.

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 pˆ ?

Square root( (0.61)(0.39)/500)

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

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?

The width of Sue's interval will be narrower than the width of Javier's interval.

A random sample of 83 residents of a certain town were asked whether they approve of a proposal to improve the town's aging bridges. The 95 percent confidence interval to estimate the proportion of all residents of the town who approve of the proposal was calculated to be (0.361,0.579).

We are 95 percent confident that the proportion of all residents in the town who favor the proposal is between 0.361 and 0.579.