Question

According to a union agreement, the mean income for all senior-level assembly-line workers in a large company equals $490 per week. A representative of a women's group decides to analyze whether the mean income for female employees matches this norm. For a random sample of nine female employees, using software, she obtains a 95% confidence interval of (464 ,498 ).

Explain what is wrong with each of the following interpretations of this interval. Complete parts a through d below.a. We infer that 95% of the women in the population have income between

$464 and $498 per week. Choose the correct answer below.

A.

The confidence interval can only be used to make inferences about the sample selected, not the population.

B.

Confidence intervals do not predict the percentage of individual people that will fall within the interval.

C.

Confidence intervals predict the percentage of randomly selected samples that would fall between the range, not the population.

D.

The confidence interval should be used to predict the income for the population of men.

b. If random samples of nine women were repeatedly selected, then 95% of the time the sample mean income would be between

$464 and $498

Choose the correct answer below.

A.

A random sample of nine women being repeatedly selected will result in the same sample mean every time.

B.

The confidence level is the percentage of the time that the confidence interval will contain the population mean, not a randomly selected sample mean.

C.

The sample size is not large enough to make inferences using a confidence interval.

D.

Using these random samples, the population mean income would be between $464 and $498 at least 95% of the time.c. We can be 95% confident that

x overbarx is between $464 and $498

Choose the correct answer below.

A.

The confidence level states that we are 95% confident that x overbarx is outside of the interval.

B.

The confidence interval for the population mean must be divided by 2 to find the confidence interval for the sample mean.

C.

We are 95% confident that x overbarx is either $464 or$498.

D.

The symbol

x overbarx ,

which represents the sample mean, should be changed to

mu? ,

which represents the population mean.d. If we repeatedly sampled the entire population, then 95% of the time the population mean would be between

$464464

and

$498498.

Choose the correct answer below.

A.

It is impossible to sample the entire population.

B.

The sample size is too large to create an accurate confidence interval for the population mean.

C.

If the entire population is sampled, we can only make a confidence interval to find the sample mean.

D.

If the entire population is sampled, then it is known exactly what the population mean is.

Click to select your answer.

Answer 1

(a)
Correct answer:

B. Confidence intervals do not predict the percentage of individual people that will fall within the interval.

(b)

Correct answer:

B. The confidence level is the percentage of time that the confidence interval contain the population mean, not a randomly selected sample mean.

(c)

Correct answer:

D.   The symbol , which represents the sample mean, should be changed to , which represents the population mean.

(d)

Correct answer:

D. If the entire population is sampled, then it is known exactly what the population mean is.