Quiz about Chapter 8 Review

Question 1

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?

Accepted Answer

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

Answer

Both populations must be approximately normal.

Answer

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

Answer

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

Question 2

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)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.

Accepted Answer

1 and 3 only

Answer

1 only

Answer

1,2, and 3 only

Answer

2 only

Question 3

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?

Accepted Answer

Question 4

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?

Accepted Answer

Question 5

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?

Accepted Answer

Question 6

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?

Accepted Answer

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

Answer

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

Answer

A one-sample Z-interval for a population proportion

Answer

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

Question 7

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?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 8

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

Accepted Answer

The data must come from populations with approximately normal distributions.

Answer

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

Answer

The samples must be selected randomly

Answer

The samples must be independent of each other.

Question 9

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?

Accepted Answer

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

Answer

Yes, all conditions for inference have been met.

Answer

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

Answer

No, because the sample was not selected at random.

Question 10

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?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 11

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?

Accepted Answer

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

Answer

No, because the size of the population is not known.

Answer

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

Answer

Yes, because the sample was selected at random.

Question 12

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?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 13

Based on a survey of a random sample of 900 adults in the United States, a journalist reports that 60 percent of adults in the United States are in favor of increasing the minimum hourly wage. If the reported percent has a margin of error of 2.7 percentage points, which of the following is closest to the level of confidence?

Accepted Answer

90.0%

Answer

99.0%

Answer

95.0%

Answer

80.0%

Question 14

The manager of a restaurant plans to survey a random sample of customers to estimate the proportion of customers who would return within a week if given a coupon for a free dessert to use on their next visit. A similar coupon was given last year, and 30 percent of the customers who were given the coupon returned within a week. The manager will use the observed proportion from last year as a preliminary estimate of the population proportion and wants the margin of error to be at most 0.04 at a 90 percent level of confidence.

Of the following, which is the least number of customers who should be surveyed such that the estimate of the margin of error of the 90 percent confidence interval will be no greater than 0.04?

Accepted Answer

370

Answer

15

Answer

260

Answer

610

Question 15

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?

Accepted Answer

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.

Answer

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.

Answer

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.

Answer

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.

Question 16

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?

Accepted Answer

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.

Answer

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.

Answer

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.

Answer

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.

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