AP Statistics Sampling Distributions 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?

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

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

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

• 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 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?

• Yes, because the sample was selected at random.

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

• Yes, because the sample is large enough to satisfy the normality conditions

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

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 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).

Which of the following is a correct interpretation of the interval?

• 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 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 sample who favor the proposal is between 0.361 and 0.579.

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.

At a particular college, 78% of all students are receiving some kind of financial aid.The school newspaper selects a random sample of 100 students and 72% of the respondents say they are receiving some sort of financial aid. Which of the following is true?

•  78% is a population and 72% is a sample.

• 72% is a population and 78% is a sample

• 78% is a parameter and 72% is a statistic

• 72% is a parameter and 78% is a statistic

30% of all dogs in a city are micro-chipped. In a sample of 500 dogs, what is the probability that less than 140 dogs are micro-chipped? Select the closest option.

• 0.25

• 0.21

• 0.17

• 0.13