Chapter 19, Problem 4E

(a)

To determine

To identify the population and the sample and explain what $p\text{ and }\widehat{p}$ represent and then tell whether the method of this can be used to create a confidence interval.

Answer to Problem 4E

The population is people who recently bought new cars and the sample is those $167$ people surveyed.

Explanation of Solution

According to the given statement in the part (a), we can say that the population is people who recently bought new cars and the sample is those $167$ people surveyed. And the $p\text{ and }\widehat{p}$ is:

  $p=$ proportion of all new cars buyers who are dissatisfied with the salesperson.

  $\widehat{p}=$ it is the proportion of those surveyed who are dissatisfied.

And we cannot use this method to apply to create a confidence interval because only five people are dissatisfied.

(b)

To determine

To identify the population and the sample and explain what $p\text{ and }\widehat{p}$ represent and then tell whether the method of this can be used to create a confidence interval.

Answer to Problem 4E

The population is college students and the sample is those students who asked about the cell phones.

Explanation of Solution

According to the given statement in the part (b), we can say that the population is college students and the sample is those students who asked about the cell phones. And the $p\text{ and }\widehat{p}$ is:

  $p=$ population proportion of college students with cell phones.

  $\widehat{p}=$ it is the proportion of those who asked with sell phones.

And the methods of this chapter cannot be applied to create a confidence interval as the sample of this is biased and non-random.

(c)

To determine

To identify the population and the sample and explain what $p\text{ and }\widehat{p}$ represent and then tell whether the method of this can be used to create a confidence interval.

Answer to Problem 4E

The population is potato plants in the U.S. and the sample is those $240$ plants.

Explanation of Solution

According to the given statement in the part (c), we can say that the population is potato plants in the U.S. and the sample is those $240$ plants. And the $p\text{ and }\widehat{p}$ is:

  $p=$ proportion of all plants in the field with blight.

  $\widehat{p}=$ it is the proportion of plants checked with blight.

And the methods of this chapter cannot be applied to create a confidence interval as the sample can be non-responsive and that can bias the result.

(d)

To determine

To identify the population and the sample and explain what $p\text{ and }\widehat{p}$ represent and then tell whether the method of this can be used to create a confidence interval.

Answer to Problem 4E

The population is employees at the company and the sample is all employees that year.

Explanation of Solution

According to the given statement in the part (d), we can say that the population is employees at the company and the sample is all employees that year. And the $p\text{ and }\widehat{p}$ is:

  $p=$ proportion of all employees who have injury on the job in a year.

  $\widehat{p}=$ it is the proportion of that year’s employees with an injury.

And the methods of this chapter cannot be applied to create a confidence interval as the sample of this is biased and non-random.