a private university claims that the overall mean earnings of its grads. roughly

Question

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.

Explanation / Answer

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

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