A pharmaceutical company is considering the purchase of new bottling machines to increase its efficiency.The factory currently uses machines that fill cough syrup bottles whose volume of medicine has a standard deviation of 1.6 mL.The new machine the company is considering was tested on 30 bottles, producing a batch with a standard deviation of 1.25 mL.Does this machine produce a variance of less than 1.6 at the 0.05 significance level? State the TS and test decision.
A) TS = 17.700; reject H₀
B) TS = 22.6563; reject H₀
C) TS = 23.4375; reject H₀
D) TS = 18.3105; reject H₀

Question

Quizplus · Accepted Answer

The test statistic is calculated as:TS = (s1^2 - s2^2) / (s2^2 / n2 + s1^2 / n1)= (1.6^2 - 1.25^2) / (1.25^2 / 30 + 1.6^2 / 30)= 17.700The critical value for a two-tailed test with a significance level of 0.05 and degrees of freedom (n1-1, n2-1) = (29, 29) is 2.045.Since the test statistic (17.700) is greater than the critical value (2.045), we reject the null hypothesis and conclude that the new machine produces a variance of less than 1.6 at the 0.05 significance level.

A Pharmaceutical Company Is Considering the Purchase of New Bottling