Chapter 12.1, Problem 66SR

To determine

To test each null hypothesis and write accept or reject.

Answer to Problem 66SR

Accepted.

Explanation of Solution

Given:

The given hypothesis is

  $H_0=55,H_1<55,n=300,\overline{x}=54.5,$ and $s=1.9$

Calculation:

The values are as follows.

  $H_0=55,H_1<55,n=300,\overline{x}=54.5,s=1.9$

The confidence level is calculated below.

  $\begin{array}{l}CI=\overline{x}\pm 1.96\cdot \frac{s}{\sqrt{n}}\\ =54.5\pm 1.96\cdot \frac{1.9}{\sqrt{300}}\\ =54.72\text{ or 54}.28\end{array}$

This means that the experience will produce a mean between $54.72$ and $54.28$ .

The confidence interval include $H_0$ , the null hypothesis will be accepted.