Chapter 8.1, Problem 18E

(a)

To determine

Check whether the explanationis correct or not.

Answer to Problem 18E

The explanation (a) there is a 95% probability that the interval from 107.8 to 116.2 contains µ is incorrect.

Explanation of Solution

Given information:

Confidence interval = 95%

Mean IQ score = 107.8 to 116.2

95% probability in the interval from 107.8 to 116.2 does notcontain true population mean $\mu$ of all sample.

Hence, the explanation (a) is incorrect.

(b)

To determine

Check whether the explanation is correct or not.

Answer to Problem 18E

The explanation (b) there is a 95% chance that the interval from 107.8 to 116.2 contains $\overline{x}$ is incorrect.

Explanation of Solution

Given information:

Confidence interval = 95%

Mean IQ score = 107.8 to 116.2

Probability that contains sample mean $\overline{x}$ is 95%. Butthe sample mean $\overline{x}$ is equal tothe center of the confidence interval. Thus the probability is 1.

Hence, the explanation(b) is incorrect.

(c)

To determine

Check whether the explanation is correct or not.

Answer to Problem 18E

The explanation (c) this interval was constructed using a method that produces intervals that capture the true mean in 95% of all possible sample is correct.

Explanation of Solution

Given information:

Confidence interval = 95%

Mean IQ score = 107.8 to 116.2

The confidence interval of 95% in the interval from 107.8 to 116.2 contains the true mean of all possible sample.

Hence, the explanation is correct.

(d)

To determine

Check whether the explanation is correct or not.

Answer to Problem 18E

The explanation (d) 95% of all possible sample will contain the interval from 107.8 to 116.2 is incorrect.

Explanation of Solution

Given information:

Confidence interval = 95%

Mean IQ score = 107.8 to 116.2

95% probability in the interval from 107.8 to 116.2 does not contain true population mean $\mu$ . Thus, the samples contains less than 95% confidence interval of all possible sample.

Hence, the explanation (d) is incorrect.

(e)

To determine

Check whether the explanation is correct or not.

Answer to Problem 18E

The explanation (e) probability that the interval from 107.8 to 116.2 captures $\mu$ is either 0 or 1, but we don’t know which is correct.

Explanation of Solution

Given information:

Confidence interval = 95%

Mean IQ score = 107.8 to 116.2

The interval from 107.8 to 116.2, the confidence interval does not contains the true population mean $\mu$ for all samples. Thus,the probability is either 0 or 1.

Hence, the explanation is correct.