Chapter 8.3, Problem 68E

(a)

To determine

To calculate: The population mean for the confidence interval of 90%.

Answer to Problem 68E

Thepopulation mean is from22.3735% to 27.1465%.

Explanation of Solution

Given information:

Sample size $n=21$

Standard deviation $s_x=6.34$

Population mean $\overline{x}=24.76$

Confidence interval $c=90\%$

Formula used:

Degree of freedom $df=n-1$

Margin of error $E=t^{*}\frac{s_x}{\sqrt{n}}$

Calculation:

Find the degree of freedom, use the formula $df=n-1$ .

  $\begin{array}{c}df=n-1\\ =21-1\\ =20\end{array}$

The confidence level is 90%.

Convert 90% into decimal.

  $\frac{90}{100}=0.90$

Find the column.

  $\begin{array}{c}\frac{1-c}{2}=\frac{1-0.90}{2}\\ =0.05\end{array}$

From table B find critical value $t^{*}$ , use the row $df$ and column.

Thus, the critical value $t^{*}\text{is}1.725$ .

Find the margin of error, use the formula $E=t^{*}\frac{s_x}{\sqrt{n}}$ .

  $\begin{array}{c}E=t^{*}\frac{s_x}{\sqrt{n}}\\ =1.725\times \frac{6.34}{\sqrt{21}}\\ =2.3865\end{array}$

Now, calculate the population mean,

  $\begin{array}{c}\overline{x}-E<\mu <\overline{x}+E\\ 24.76-2.3865<\mu <24.76+2.3865\\ 22.3735<\mu <27.1465\end{array}$

Hence, the required population mean is from 22.3735% to 27.1465%.

(b)

To determine

Explain the effect of the confidence interval for the survey of that one patient.

Answer to Problem 68E

The confidence interval cannot be generalizing for the sample population.

Explanation of Solution

From 68(a)confidence interval contain the population mean from22.3735% to 27.1465%.Since the confidence interval lies above 0.

Hence, the confidence interval cannot be generalizing for that one patient with HAV angle of 50 degrees.