a private university claims that the overall mean earnings o

a private university claims that the overall mean earnings of its grads. roughly equal 75,00 per year with a standard deviation of 15,000 per year. the five senses bureau does a random sample of 900 of the grads and find the sample mean to be 74,000. perform a two tailed hypothesis test of the claim of the university being accuarate using a 5 % risk of a type 1 error or A<0.05. be sure to state the null and alternative hypothesis clearly and make sure that your reasons for accepting or rejecting the null hypothesis are clear.

Solution

Let mu be the population mean

Null hypothesis: mu=75,000

Alternative hypothesis: mu not equal to 75,000

The test statistic is

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

=(74000-75000)/(15000/sqrt(900))

=-2

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 iZ<-1.96 or Z>1.96, we reject the null hypothesis.

Since Z=-2 is less than -1.96, we reject the null hypothesis.

So we cannot conclude that the overall mean earnings of its grads. roughly equal 75,00 per year