A large industrial customer complains to its electric supplier that the variance in voltage supplied to its facility exceeds the promised value of 255.The electric supplier takes 30 voltage measurements at differing times of the day and finds a sample variance of 244.Does the sample indicate that the population variance is significantly less than 255? State the critical value (CV), test statistic (TS), and decision from the test.(Use α = 0.10.)
A) CV = -19.7677; TS = 27.749; fail to reject H₀
B) CV = 14.2565; TS = 30.307; fail to reject H₀
C) CV = 19.7677; TS = 27.749; fail to reject H₀
D) CV = 39.0875; TS = 30.307; fail to reject H₀

Question

Quizplus · Accepted Answer

To test whether the sample variance provides enough evidence to reject the claim that the population variance exceeds 255, we can use a chi-square test with (n-1) degrees of freedom, where n is the sample size. With a significance level of 0.10, and (n-1) = 29 degrees of freedom, the critical value is 19.7677. From the information given, the test statistic is calculated as follows:

TS = (n-1)S^2/σ^2 = (30-1)(244)/255 = 27.749

Since the test statistic (TS) is less than the critical value (CV), we fail to reject the null hypothesis (H₀) that the population variance is greater than 255. Therefore, the best choice is C.

A Large Industrial Customer Complains to Its Electric Supplier That