A researcher wishes to test the claim that the average cost

A researcher wishes to test the claim that the average cost of tuition and fees at a four-year public college is greater than $5700. She selects a random sample of 36 four-year public colleges and finds the mean to be $5950. The population standard deviation is $659. Is there evidence to support the claim at . Use the traditional method of hypothesis testing (show all 5 steps).

Solution

State the hypotheses and identify the claim.
H0: µ = $5700 and H1: µ> $5700

Compute the test value.
z=(xbar-mu)/sigma/sqrt(n)=5950 5700/659/sqrt(36)=2.28

the area for z = 2.28.The area is 0.9887.Subtract from 1.0000 to find the area of the tail.Hence, the
P-value is 1.0000 – 0.9887 = 0.0113.

Since the p value is less than 0.05, decision on is to reject Ho.

There is enough evidence to support the claim that
the tuition and fees at four-year public colleges are
greater than $5700