Chapter 23, Problem 5E

(a)

To determine

To find out did anyone interpret the interval correctly for the following conclusion and explain any misinterpretations.

Answer to Problem 5E

It is incorrect.

Explanation of Solution

Livestock are given special feed supplement to see if it will promote weight gain. Researchers report that the $77$ cows studied gained an average of $56$ pounds and that a $95\%$ confidence interval for the mean weight gain. Therefore some students wrote the conclusion for the following study.

The first conclusion is: $95\%$ of the cows studied gained between $45\text{ and 67}$ pounds. This conclusion is incorrect because the given confidence interval is for the population mean and not for individual observations.

(b)

To determine

To find out did anyone interpret the interval correctly for the following conclusion and explain any misinterpretations.

Answer to Problem 5E

It is incorrect.

Explanation of Solution

Livestock are given special feed supplement to see if it will promote weight gain. Researchers report that the $77$ cows studied gained an average of $56$ pounds and that a $95\%$ confidence interval for the mean weight gain. Therefore some students wrote the conclusion for the following study.

The second conclusion is: We are $95\%$ sure that a cow fed this supplement will gain between $45\text{ and 67}$ pounds. This conclusion is incorrect because the given confidence interval is for the population mean and not for individual observations.

(c)

To determine

To find out did anyone interpret the interval correctly for the following conclusion and explain any misinterpretations.

Answer to Problem 5E

It is incorrect.

Explanation of Solution

Livestock are given special feed supplement to see if it will promote weight gain. Researchers report that the $77$ cows studied gained an average of $56$ pounds and that a $95\%$ confidence interval for the mean weight gain. Therefore some students wrote the conclusion for the following study.

The third conclusion is: we are $95\%$ sure that the average weight gain among the cows in the study was between $45\text{ and 67}$ pounds. This conclusion is incorrect because we are $100\%$ sure that the average weight gain among the cows in this study was between $45\text{ and 67}$ pounds, since the average weight gain in this study was $56$ pounds.

(d)

To determine

To find out did anyone interpret the interval correctly for the following conclusion and explain any misinterpretations.

Answer to Problem 5E

It is incorrect.

Explanation of Solution

Livestock are given special feed supplement to see if it will promote weight gain. Researchers report that the $77$ cows studied gained an average of $56$ pounds and that a $95\%$ confidence interval for the mean weight gain. Therefore some students wrote the conclusion for the following study.

The fourth conclusion is: the average weight gain of cows fed this supplement will be between $45\text{ and 67}$ pounds $95\%$ of the time. This conclusion is incorrect because the average weight gain of all cows will not vary.

(e)

To determine

To find out did anyone interpret the interval correctly for the following conclusion and explain any misinterpretations.

Answer to Problem 5E

It is incorrect.

Explanation of Solution

Livestock are given special feed supplement to see if it will promote weight gain. Researchers report that the $77$ cows studied gained an average of $56$ pounds and that a $95\%$ confidence interval for the mean weight gain. Therefore some students wrote the conclusion for the following study.

The fifth conclusion is: if this supplement is tested on another sample of cows, there is a $95\%$ chance that their average weight gain will be between $45\text{ and 67}$ pounds. This conclusion is incorrect because we know that there is a $95\%$ chance that the average weight gain is within two standard deviation of the population mean, but not within two standard deviation of the sample mean of another sample.