A researcher wishes to test the claim that the average cost

A researcher wishes to test the claim that the average cost of books per semester at a four-year college is $970. She selects a random sample of 25 four-year colleges and finds the mean to be $925. The population standard deviation is $70. Is there enough evidence to support the claim at ? = .05?

Solution

Let mu be the population mean

Ho: mu=970 (i.e. null hypothesis)

Ha: mu not equal to 970 (i.e. alternative hypothesis)

The test statistic is

Z=(xbar-mu)/(s/vn)

=(925-970)/(70/sqrt(25))

=-3.21

It is a two-tailed test.

Given a=0.05, the critical values are Z(0.025) = -1.96 or 1.96 (from standard normal table)

The rejection regions are if Z<-1.96 or Z>1.96, we reject the null hypothesis.

Since Z=-3.21 is less than -1.96, we reject the null hypothesis.

So we cannot conclude that the average cost of books per semester at a four-year college is $970