Chapter 9.3, Problem 77E

To determine

To find: Whether there is sufficient evidence to show that the mean hardness is different from the targeted value of 11.5 at 5% significance level.

Answer to Problem 77E

No, there sufficient evidence to show that the mean hardness is different from the targeted value.

Explanation of Solution

Given:

The data set is:

11.627
11.613
11.493
11.602
11.36
11.374
11.592
11.458
11.552
11.463
11.383
11.715
11.485
11.509
11.429
11.477
11.57
11.623
11.472
11.531

Formula used:

The test statistic formula is:

  $t=\frac{\overline{x}-{\mu }_o}{\frac{s}{\sqrt{n}}}$

Calculation:

The null and alternative hypotheses are:

  $\begin{array}{l}{H}_0:\mu =11.5\\ H_a:\mu \ne 11.5\end{array}$

The alternative hypothesis represents that the test is two tailed.

The obtained Minitab output is:

  

The p -value is 0.449.

Here, $p\text{-value}\left(0.449\right)>\alpha \left(0.05\right)$ . The null hypothesis is not rejected.

Conclusion:

At 5% level of significance there is insufficient evidence to show that the mean hardness of the tablets is different from the targeted value of 11.5