Chapter 8.1, Problem 17E

(a)

To determine

Check whether the explanation is correct or not.

Answer to Problem 17E

The explanation (a) we are confidence that 95% of all young women have BMI between 26.2 and 27.4 is incorrect.

Explanation of Solution

Given information:

Confidence interval = 95%

Body mass index (BMI) = $26\pm 0.6$

  $\begin{array}{l}\text{Body}\text{mass}\text{index}\left(\text{BMI}\right)\text{=}\text{26}\text{±}\text{0}\text{.6}\\ \text{=}\text{26}\text{.2}\text{and}\text{27}\text{.4}\end{array}$

In this statement the confidence interval is givenonly for young.

Hence, the explanation (a) is incorrect.

(b)

To determine

Check whether the explanation is correct or not.

Answer to Problem 17E

The explanation (b)we are 95% confidence that future sample of young women will have mean BMI between 26.2 and 27.4 is incorrect.

Explanation of Solution

Given information:

Confidence interval = 95%

Body mass index (BMI) = $26\pm 0.6$

  $\begin{array}{l}\text{Body}\text{mass}\text{index}\left(\text{BMI}\right)\text{=}\text{26}\text{±}\text{0}\text{.6}\\ \text{=}\text{26}\text{.2}\text{and}\text{27}\text{.4}\end{array}$

Since confidence intervals for the future samples may vary. It is not possible to say that the true mean BMI will lie between 26.2 and 27.4.

Hence, the explanation (b) is incorrect.

(c)

To determine

Check whether the explanation is correct or not.

Answer to Problem 17E

The explanation (c) any value from 26.2 and 27.4 is believable as the true mean BMI of young American women is correct.

Explanation of Solution

Given information:

Confidence interval = 95%

Body mass index (BMI) = $26\pm 0.6$

  $\begin{array}{l}\text{Body}\text{mass}\text{index}\left(\text{BMI}\right)\text{=}\text{26}\text{±}\text{0}\text{.6}\\ \text{=}\text{26}\text{.2}\text{and}\text{27}\text{.4}\end{array}$

True mean BMI lies between 26.2 and 27.4. Thus,it can be assume that that any value between 26.2 and 27.4 is believable as the true mean BMI.

Hence, the explanation (c) is correct.

(d)

To determine

Check whether the explanation is correct or not.

Answer to Problem 17E

The explanation (d) in 95% of all possible sample, the population mean BMI will be between 26.2 and 27.4 is incorrect.

Explanation of Solution

Given information:

Confidence interval = 95%

Body mass index (BMI) = $26\pm 0.6$

  $\begin{array}{l}\text{Body}\text{mass}\text{index}\left(\text{BMI}\right)\text{=}\text{26}\text{±}\text{0}\text{.6}\\ \text{=}\text{26}\text{.2}\text{and}\text{27}\text{.4}\end{array}$

95% confidence interval contains the true mean BMI which lie between the interval 26.2 and 27.4. Remaining 5% samples does not contain the true mean BMI.

Hence, the explanation (d) is incorrect.

(e)

To determine

Check whether the explanation is correct or not.

Answer to Problem 17E

The explanation (e) the mean BMI of young American women cannot be 28 is incorrect.

Explanation of Solution

Given information:

Confidence interval = 95%

Body mass index (BMI) = $26\pm 0.6$

  $\begin{array}{l}\text{Body}\text{mass}\text{index}\left(\text{BMI}\right)\text{=}\text{26}\text{±}\text{0}\text{.6}\\ \text{=}\text{26}\text{.2}\text{and}\text{27}\text{.4}\end{array}$

In this explanation the population mean is unknown.Thus,mean BMI may not be equal to 28.

Hence, the explanation (e) is incorrect.