Question

A university claims that the mean time professors are in their offices for students is at least 6.5 hours each week. A random sample of eight professors finds that the mean time in their offices is 6.2 hours each week. With a sample standard deviation of 0.49 hours from a normally distributed data set, can the university’s claim be supported at α=0.05?

A. Yes, since the test statistic is not in the rejection region defined by the critical value, the null is not rejected. The claim is the null, so is supported

B. No, since the test statistic is not in the rejection region defined by the critical value, the null is rejected. The claim is the null, so is not supported

C. Yes, since the test statistic is in the rejection region defined by the critical value, the null is not rejected. The claim is the null, so is supported

D. No, since the test statistic is in the rejection region defined by the critical value, the null is rejected. The claim is the null, so is not supported

Answer 1

H0: >= 6.5

Ha: < 6.5

Test statistics

t = - / S / sqrt(n)  

= 6.2 - 6.5 / 0.49 / sqrt(8)

= -1.73

This is test statistics value.

Critical value at 0.05 level with 7 df = -1.895

Since test statistics falls in on-rejection region, we do not have sufficient evidence to reject H0.

We conclude that,

No, since the test statistic is not in the rejection region defined by the critical value, the null is rejected.

The claim is the null, so is not supported