Question

Pressing pills A drug manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The hardness of a sample from each batch of tablets produced is measured to control the compression process. The target value for the hardness is $\mu =11.5$The hardness data for a random sample of 20 tablets from one large batch are

Is there convincing evidence at the $5\%$level that the mean hardness of the tablets in this batch differs from the target value?

Short answer

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

Step-by-step solution

Given information

The data set is:

The objective is to find whether there is sufficient evidence to show that the mean hardness is different from the targeted value of 11.5at 5%the significance level.

We know,

The test statistic formula is: $t=\frac{\overline{x}-{\mu }_o}{\frac{s}{\sqrt{n}}}$

The null and alternative hypotheses are as follows:

$$\begin{gathered} H_0:\mu =11.5 \\ {H}_a:\mu notequalto11.5 \end{gathered}$$

The alternative hypothesis denotes a two-tailed test.

The Minitab output is as follows:

The $p$-value is $0.449$

Here, $p$-value $(0.449)>\alpha (0.05)$The null hypothesis does not fail.

There is insufficient evidence at the $5\%$level of significance to show that the mean hardness of the tablets differs from the target value of$11.5.$