Chapter 9.3, Problem 93E

a.

To determine

To find: Whether the result is significance at 5% level of significance.

Answer to Problem 93E

No, it is not significant.

Explanation of Solution

Given:

  $\begin{array}{l}\text{Sample mean}\left(\overline{x}\right)=536.7\\ \text{Sample standard deviation}\left(s_x\right)=114\\ \text{Sample size}\left(n\right)=100\end{array}$

The hypotheses are:

  $\begin{array}{l}{H}_0:\mu =518\\ H_a:\mu >518\end{array}$

Calculation:

The obtained Ti-83 output is:

  

The p-value is more than the significance level. Thus, the null hypothesis cannot be rejected.

At 5% significance level, there are insufficient evidence to support the provided claim that the test is significant.

b.

To determine

To find: Whether the result is significance at 5% level of significance.

Answer to Problem 93E

Yes, it is significant.

Explanation of Solution

Given:

  $\begin{array}{l}\text{Sample mean}\left(\overline{x}\right)=537.0\\ \text{Sample standard deviation}\left(s_x\right)=114\\ \text{Sample size}\left(n\right)=100\end{array}$

The hypotheses are:

  $\begin{array}{l}{H}_0:\mu =518\\ H_a:\mu >518\end{array}$

Calculation:

The obtained Ti-83 output is:

  

The p-value is less than the significance level. Thus, the null hypothesis can be rejected.

At 5% significance level, there are sufficient evidence to support the provided claim that the test is significant.

c.

To determine

To explain: The conclusion that could be drawn using the result of above two parts.

Explanation of Solution

From above parts, it is known that all values are same except the values of the mean, Thus, it could be said that the small change in the value of the sample mean could change the result of overall hypothesis testing.