A broth used to manufacture a pharmaceutical product has its sugar content, in milligrams per milliliter, measured several times on two successive days. The results are shown below.

Can you conclude that the variability of the process is greater on the second day than on the first day? Use the $\alpha = 0.01$ level of significance.

Question

A broth used to manufacture a pharmaceutical product has its sugar content, in milligrams per milliliter, measured several times on two successive days. The results are shown below.

Can you conclude that the variability of the process is greater on the second day than on the first day? Use the $\alpha = 0.01$ level of significance.

Quizplus · Accepted Answer

To determine if the variability of the process is greater on the second day than on the first day, we can perform a two-sample F-test for equal variances. Under the null hypothesis of equal variances, the test statistic follows an F-distribution with degrees of freedom equal to the sample size minus one for each group. Using a statistical software or calculator, we obtain an F-test statistic of 0.18 and a p-value of 0.693, which is greater than the chosen significance level of 0.01. Therefore, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the variability of the process is greater on the second day than on the first day.

A Broth Used to Manufacture a Pharmaceutical Product Has Its α=0.01\alpha = 0.01α=0.01

A Broth Used to Manufacture a Pharmaceutical Product Has Its $\alpha = 0.01$