Question

Cans of coke for the sample data from exercise 1, we get “P-value<0.01” when testing the claim that the new filling process results in volumes with the same standard deviation of 0.115 oz.

1. What should we conclude about the null hypothesis?
2. What should we conclude about the original claims?
3. What do these results suggest about the new filling process?

Short answer

a. The null hypothesis is rejected ata0.01 level of significance.

b. There is notsufficient evidence to support the null hypothesis.

c. The result suggests that the variation in the volume is different from 0.115 oz, which implies the volume is not consistent.

Step-by-step solution

Step-1: Given information

Refer to the data in exercise 1 for the volume of the new filling process.

Step-2: State the hypotheses

a.

Let $\sigma$be the population standard deviation of the volumes of new filling processes.

$$\begin{gathered} H_0:\sigma =0.115 \\ {H}_1:\sigma \ne 0.115 \end{gathered}$$

Step-3: State the decision

b.

The decision rule statesif the p-value is lesser than 0.01, the null hypothesis is rejected. Otherwise, the null hypothesis is failed to be rejected.

The p-value is lesser than 0.01. Thus, the null hypothesis is rejected. Hence, it can be concluded that there is not sufficient evidence to support the claim.

Step-4: Compute the test statistic

c.

The result suggests that the volume is inconsistent throughout all cans from the new filling process. Thus, the standard deviation is different from 0.115 oz.