Auniversity 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?

Let be the population mean.

Null hypothesis :

Alternative hypothesis :

Since alternative hypothesis is left-tailed , so the test is a left-tailed test.

Since n= 8 <30 , so we use t-test.

Test statistic for population mean :

Critical value for t=

Since the absolute t-value (1.73) is less than the critical t-value(1.895), it means we are fail to reject the null hypothesis.

Thus , we conclude that we have enough evidence to support the university’s claim.