One Proportion Z Interval

A school administrator is interested in estimating the proportion of students in the district who participate in community service activities. From a random sample of 100 students in the district, the administrator will construct a 99 percent confidence interval for the proportion of all district students who participate in community service activities. Which of the following statements must be true?

• The population proportion will be in the confidence interval.

• The probability that the confidence interval will include the population proportion is 0.99.

• The probability that the confidence interval will include the sample proportion is 0.99.

• The population proportion and the sample proportion will be equal

• The probability that the population proportion and the sample proportion will be equal is 0.99.

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?

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?

• one-sample z-interval for a sample proportion

• one-sample z-interval for a population proportion

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

• two-sample z-interval for a difference between sample proportions

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

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?

• one-sample z-interval for a sample proportion

• one-sample z-interval for a population proportion

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

• two-sample z-interval for a difference between sample proportions

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

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.

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

• 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 wider than 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

• 36 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 (constant), but the sample proportion p-hat can vary from sample to sample.

• The interval either does or does not capture p.

• There is a 0.95 probability that the proportion of all residents in the town who favor the proposal will be between 0.361 and 0.579.

• The probability that 95 percent of the residents in the town will favor the proposal is between 0.361 and 0.579.

• We are 95 percent confident that any sample of 83 residents will produce a sample proportion between 0.361 and 0.579.

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

A 90% confidence interval for the proportion different p1-p2 was calculated to be (0.247, 0.325). Which of the following conclusions is supported by the interval?

• There is evidence to conclude that p1>p2 because 0.325 is greater than 0.247.

• There is evidence to conclude that p1<p2 because 0.325 is greater than 0.247.

• There is evidence to conclude that p1>p2 because all values in the interval are positive.

• There is evidence to conclude that p1<p2 because all values in the interval are positive.

• There is evidence to conclude that p2>p1 because 0.247 and 0.325 are both greater than 0.05.

Which condition, if met, says the sampling distribution of p-hat will be approximately normal?

• Random Sample

• 10% Condition

• Large Counts condition