Chapter 8.3, Problem 61E

(a)

To determine

To calculate: The standard deviation $s_x$ .

Answer to Problem 61E

The standard deviation is91.2647.

Explanation of Solution

Given information:

Sample size $n=23$

Standard error of mean $SE=19.03$

Formula used:

Standard error of mean $SE=\frac{s_x}{\sqrt{n}}$

Calculation:

Standard error of mean is $SE=\frac{s_x}{\sqrt{n}}$ .

Multiply both side by $\sqrt{n}$ .

  $\begin{array}{c}s=SE\times \sqrt{n}\\ =19.03\times \sqrt{23}\\ =91.2647\end{array}$

Hence, the required standard deviation is 91.2647.

(b)

To determine

Explain the reason why the given interval is not a confidence interval.

Answer to Problem 61E

The given interval is not a confidence interval

Explanation of Solution

Formula used:

The confidence interval = $\overline{x}\pm \left(t^{*}\times \overline{E}\right)$

The formula for the confidence interval is $\overline{x}\pm \left(t^{*}\times \overline{E}\right)$ .

In the problem interval is $\overline{x}\pm \overline{E}$ . Since $t^{*}$ is unknown.

Hence, the given interval is not a confidence interval.