Chapter 19, Problem 3E

(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 3E

The population is all cars and the sample is those actually stopped at the check point.

Explanation of Solution

According to the given statement in the part (a), we can say that the population is all cars and the sample is those actually stopped at the check point. And the $p\text{ and }\widehat{p}$ is:

  $p=$ proportion of all cars with safety problems.

  $\widehat{p}=$ it is the proportion actually seen with safety problems.

And if the sample is representative then the methods of this chapter will apply to create a confidence interval.

(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 3E

The population is general public and the sample is those who logged the web site.

Explanation of Solution

According to the given statement in the part (b), we can say that the population is general public and the sample is those who logged the web site. And the $p\text{ and }\widehat{p}$ is:

  $p=$ population proportion of those who favor prayer in school.

  $\widehat{p}=$ it is the proportion of those who voted in the poll who favored prayer in the school.

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 3E

The population is parents at the school and the sample is those who returned the questionnaire.

Explanation of Solution

According to the given statement in the part (c), we can say that the population is parents at the school and the sample is those who returned the questionnaire. And the $p\text{ and }\widehat{p}$ is:

  $p=$ proportion of all parents who favor uniforms.

  $\widehat{p}=$ it is the proportion of respondents who favor uniforms.

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 3E

The population is students at the college and the sample is the students who entered that year.

Explanation of Solution

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

  $p=$ proportion of all students who will graduate in time.

  $\widehat{p}=$ it is the proportion of that year’s students who graduate on time.

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