Chapter 8 Review

Consider a situation in which sampling without replacement is used to generate a random sample from each of two separate populations. To calculate a confidence interval to estimate the difference between population proportions, which of the following checks must be made?

• Each population must be at least 10 times as large as its corresponding sample.

• Both populations must be approximately normal.

• The data from both samples must be unimodal, symmetrical, and approximately normal.

• Each sample proportion value must be less than or equal to 0.5.

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A gardener wants to know if soaking seeds in water before planting them increases the proportion of seeds that germinate. To investigate, the gardener will assign 50 seeds to be soaked before planting and 50 seeds to be planted without being soaked. After two weeks, the gardener will record how many seeds in each group germinated and construct a 95 percent confidence interval for the difference in proportions. Which of the following conditions for inference should be met?

1. 1)The seeds should be randomly assigned to a treatment.

2. 2)The group sizes should be less than 10 percent of the population sizes.

3. 3)The number of successful seeds and unsuccessful seeds in each group should be at least 10.

• 1 only

• 1,2, and 3 only

• 1 and 3 only

• 2 only

As part of a national sleep study, a random sample of adults was selected and surveyed about their physical activity and the number of hours they sleep each night. Of the 183 adults who exercised regularly (exercisers), 59 percent reported sleeping at least seven hours at night. Of the 88 adults who did not exercise regularly (nonexercisers), 52 percent reported sleeping at least seven hours at night. Which of the following is the most appropriate standard error for a confidence interval for the difference in proportions of adults who sleep at least seven hours at night among exercisers and nonexercisers?

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Researchers are studying the distribution of subscribers to a certain streaming service in different populations. From a random sample of 200 people in City C, 34 were found to subscribe to the streaming service. From a random sample of 200 people in City K, 54 were found to subscribe to the streaming service. Assuming all conditions for inference are met, which of the following is a 90 percent confidence interval for the difference in population proportions (City C minus City K) who subscribe to the streaming service?

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There are 1,000 golden delicious and 1,000 red delicious apples in a cooler. In a random sample of 75 of the golden delicious apples, 48 had blemishes. In a random sample of 75 of the red delicious apples, 42 had blemishes. Assume all conditions for inference have been met. Which of the following is closest to the interval estimate of the difference in the numbers of apples with blemishes (golden delicious minus red delicious) at a 98 percent level of confidence?

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Two large containers, X and Y, contain many colored beads. From a random sample of beads taken from container X, the proportion of blue beads in the sample was recorded as P^X=0.35. From a random sample of beads taken from container Y, the proportion of blue beads in the sample was recorded as P^Y=0.39. Assuming all conditions for inference are met, which of the following procedures is the most appropriate for estimating the difference between the proportions of all blue beads in the containers?

• A one-sample Z-interval for a difference in population proportions

• A one-sample Z-interval for a population proportion

• A two-sample Z-interval for a difference in sample proportions

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

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A researcher calculated sample proportions from two independent random samples. Assuming all conditions for inference are met, which of the following is the best method for the researcher to use to estimate the true difference between the population proportions?

• Construct a two-sample Z-interval for the difference between sample proportions.

• Construct a two-sample Z-interval for the difference between population proportions.

• Subtract the proportions and construct a one-sample Z-interval for a single population proportion.

• Subtract the proportions and construct a Z-interval for a single sample proportion.

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Independent random samples of voters from two voting districts, G and H, were selected to investigate the proportion of all voters who favor a proposal to widen a road that runs through both districts. The difference between the sample proportions (G minus H) was used to create the 95 percent confidence interval (0.13,⁢0.47) for the population difference between districts.

Which of the following is the best interpretation of the interval?

• It is likely that the majority of voters in both districts favor the proposal, because all values in the interval are positive.

• It is likely that more voters in district H favor the proposal than in district G, because all values in the interval are positive.

• It is likely that more voters in district G favor the proposal than in district H, because all values in the interval are positive.

• It is likely that less than half the voters in both districts favor the proposal, because all values in the interval are less than 0.5.

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Which of the following is not a condition for constructing a confidence interval to estimate the difference between two population proportions?

• When samples are taken without replacement, each population must be at least 10 times as large as its corresponding sample

• The samples must be selected randomly

• The samples must be independent of each other.

• The data must come from populations with approximately normal distributions.

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Researchers from a national research organization investigated which platform (television, social media, newspaper, Internet, etc.) United States adults prefer to use to obtain their news. In 2016, of the 200 randomly selected United States adults that were surveyed, 114 selected television as their preferred platform. In 2018, of the 200 randomly selected United States adults that were surveyed, 98 selected television as their preferred platform. The conditions for inference are met. A 95 percent confidence interval for the difference in the population proportions of United States adults that use television as their preferred platform for obtaining news between 2016 and 2018 (2016⁢⁢ minus 2018) was found to be (-0.02,0.18).

Based on the interval, is it reasonable for the researchers to claim that there is convincing statistical evidence that the population proportion of United States adults that use television as their preferred method to obtain news differed between 2016 and 2018 ?

• Yes, because zero is included in the interval there is convincing statistical evidence that the population proportion differed between 2016 and 2018.

• No, because the researchers should have used a greater confidence level to obtain convincing evidence.

• No, because zero is included in the interval there is not convincing statistical evidence that the population proportion differed between 2016 and 2018.

• Yes, because most of the interval is positive there is convincing statistical evidence that the population proportion increased from 2016 to 2018.

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