Chapter 23, Problem 9E

(a)

To determine

To explain carefully what the software input means.

Explanation of Solution

It is given that a medical researcher measured the pulse rates (beats per minute) of a sample of randomly selected adults and found the following student’s t -based confidence interval, that is:

  $\begin{array}{l}\text{With 95\% Confidence,}\\ 70.887604<\mu <74.497011\\ \mu =\text{ Pulse}\end{array}$

By looking at the software output, we can say that we are looking at the two standard deviations away from the center to find $\text{95}$ percent confidence, which shows that the mean pulse rate of adults is between $\text{70}\text{.9 and 74}\text{.5}$ beats per minute.

(b)

To determine

To find out what is the margin of error for this interval.

Answer to Problem 9E

The margin of error is $1.8$ beats per minute.

Explanation of Solution

It is given that a medical researcher measured the pulse rates (beats per minute) of a sample of randomly selected adults and found the following student’s t -based confidence interval, that is:

  $\begin{array}{l}\text{With 95\% Confidence,}\\ 70.887604<\mu <74.497011\\ \mu =\text{ Pulse}\end{array}$

The margin of error can be calculated as:

  $\begin{array}{l}\text{Margin of error}=\frac{74.5-70.9}{2}\\ =\frac{3.6}{2}\\ =1.8\end{array}$

Thus, the margin of error is $1.8$ beats per minute.

(c)

To determine

To explain what would the margin of error be larger or smaller, if the researcher has calculated a $99\%$ confidence interval.

Answer to Problem 9E

It will be larger.

Explanation of Solution

It is given that a medical researcher measured the pulse rates (beats per minute) of a sample of randomly selected adults and found the following student’s t -based confidence interval, that is:

  $\begin{array}{l}\text{With 95\% Confidence,}\\ 70.887604<\mu <74.497011\\ \mu =\text{ Pulse}\end{array}$

And the margin of error is $1.8$ beats per minute. Now, if the researcher has calculated a $99\%$ confidence interval then the margin of error will be larger because a margin of error tells us how many percentage points our results will differ from the real population value.