A local arts council has 200 members. The council president wanted to estimate the percent of its members who have had experience in writing grants. The president randomly selected 30 members and surveyed the selected members on their grant-writing experience. Of the 30 selected members, 12 indicated that they did have the experience. Have the conditions for inference with a one-sample Z-interval been met?

No, because the sample size is not less than 10 percent of the population size.

Yes, all conditions for inference have been met.

No, because the sample size is not large enough to satisfy the conditions for normality.

No, because the sample was not selected at random.

From a random sample of potential voters in an upcoming election, 47% indicated they intended to vote for Candidate R. A 95 percent confidence interval was constructed from the sample, and the margin of error for the estimate was 5%. Which of the following is the best interpretation of the interval?

We are 95% confident that the proportion who intend to vote for Candidate R from the population is between 42% and 52%.

We are 95% confident that the proportion who intend to vote for Candidate R from the random sample is between 42% and 52%.

We are 95% confident that the proportion who intend to vote for Candidate R from the random sample is 47%.

We are 95% confident that the proportion who intend to vote for Candidate R from the population is 47%.

A random sample of residents in city J were surveyed about whether they supported raising taxes to increase bus service for the city. From the results, a 95 percent confidence interval was constructed to estimate the proportion of people in the city who support the increase. The interval was (0.46,⁢0.52). Based on the confidence interval, which of the following claims is supported?

More than 40 percent of the residents support the increase.

More than 90 percent of the residents support the increase.

More than 60 percent of the residents support the increase.

Fewer than 10 percent of the residents support the increase.

A city planner wants to estimate the proportion of city residents who commute to work by subway each day. A random sample of 30 city residents was selected, and 28 of those selected indicated that they rode the subway to work. 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 is large enough to satisfy the normality conditions.

Yes, because the sample was selected at random.

An environmental group wanted to estimate the proportion of fresh produce sales identified as organic in a local grocery store. In the winter, the group obtained a random sample of sales from the store and used the data to construct the 95 percent z -interval for a proportion (0.087, 0.133 ). Six months later in the summer, the group obtained a second random sample of sales from the store. The second sample was the same size as the first, and the proportion of sales identified as organic was 0.4. How does the 95 percent z -interval for a proportion constructed from the summer sample compare to the winter interval?

The summer interval is wider and has a greater point estimate.

The summer interval is wider and has a lesser point estimate.

The summer interval is narrower and has a lesser point estimate.

The summer interval is narrower and has a greater point estimate.

Elly and Drew work together to collect data to estimate the percentage of their classmates who own a particular brand of shoe. Using the same data, Elly will construct a 90 percent confidence interval and Drew will construct a 99 percent confidence interval. Which of the following statements is true?

The width of Elly’s interval will be less than the width of Drew’s interval.

The width of Elly’s interval will be greater than the width of Drew’s interval.

The midpoint of Elly’s interval will be less than the midpoint of Drew’s interval.

The midpoint of Elly’s interval will be greater than the midpoint of Drew’s interval.

A polling agency reported that 66 percent of adults living in the United States were satisfied with their health care plans. The estimate was taken from a random sample of 1,542 adults living in the United States, and the 95 percent confidence interval for the population proportion was calculated as (0.636, 0.684). Which of the following statements is a correct interpretation of the 95 percent confidence level?

Approximately 95% of random samples of the same size from the population will result in a confidence interval that includes the proportion of all adults living in the United States who are satisfied with their health care plans.

Approximately 95% of random samples of the same size from the population will result in a confidence interval that includes the proportion of all adults in the sample who are satisfied with their health care plans.

Approximately 95% of all random samples of adults living in the United States will indicate that between 63.6% and 68.4% of the adults are satisfied with their health care plans.

Approximately 95% of all random samples of adults living in the United States will result in a sample proportion of 0.66 adults living in the United States who are satisfied with their health care plans.

On the day before an election in a large city, each person in a random sample of 1,000 likely voters is asked which candidate he or she plans to vote for. Of the people in the sample, 55 percent say they will vote for candidate Taylor. A margin of error of 3 percentage points is calculated. Which of the following statements is appropriate?

The sample proportion minus the margin of error is greater than 0.50, which provides evidence that more than half of all likely voters plan to vote for candidate Taylor.

The proportion of all likely voters who plan to vote for candidate Taylor must be the same as the proportion of voters in the sample who plan to vote for candidate Taylor (55 percent), because the data were collected from a random sample.

It is not possible to draw any conclusion about the proportion of all likely voters who plan to vote for candidate Taylor because the 1,000 likely voters in the sample represent only a small fraction of all likely voters in a large city.

It is not possible to draw any conclusion about the proportion of all likely voters who plan to vote for candidate Taylor because this is not an experiment.

Chapter 8 Review Quiz

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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.

Tags

CCSS.HSS.IC.B.4

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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)The seeds should be randomly assigned to a treatment.
2)The group sizes should be less than 10 percent of the population sizes.
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

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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?

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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?

Tags

CCSS.HSS.IC.B.4

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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?

Tags

CCSS.HSS.IC.B.4

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

Tags

CCSS.HSS.IC.B.4

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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.

Tags

CCSS.HSS.IC.B.4

8.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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.

Tags

CCSS.HSS.IC.B.4

9.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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.

Tags

CCSS.HSS.IC.B.4

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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.

Tags

CCSS.HSS.IC.B.4

Chapter 8 Review

20 questions

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?

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?

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

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