Chapter 10.2, Problem 10.46E

(a)

To determine

To Calculate: and interpret a 95% interval for the mean blood pressure of the population from which the subjects were recruited.

Answer to Problem 10.46E

(111.2202, 118.5798)

There is 99% confident that the mean blood pressure is between $111.2202$ and $118.5798$ .

Explanation of Solution

Given:

  $\begin{array}{c}n=27\\ \overline{x}=114.9\\ s=9.3\\ c=95\%=0.95\end{array}$

Formula used:

  $E=z_{a/2}\times \frac{s}{\sqrt{n}}$

Calculation:

The t-value by looking in the row starting with degrees of freedom $df=n-1=27-1=26$ and in the column with $p=\left(1-c\right)/2=0.025$ in the table of the students’ $T$ distribution: $t^{\ast }=2.056$

The margin of error is

  $E=t_{a/2}\times \frac{s}{\sqrt{n}}=2.056\times \frac{93}{\sqrt{27}}=3.6798$

Confidence intervals

  $\begin{array}{c}\overline{x}-E=114.9-3.6798=111.2202\\ \overline{x}-E=114.9+3.6798=118.5798\end{array}$

There is 99% confident that the mean blood pressure is between $111.2202$ and $118.5798$ .

(b)

To determine

To Explain: requires an important assumption about the 27 men who provided the data.

Answer to Problem 10.46E

No outliers and no strong skewed

Explanation of Solution

The required assumption to get the 95% confidence interval is that the sample has no outliers and no strong skewed.