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 \(\alpha=0.05\)? Use the P-value method.

Step 1:

State the Hypothesis

\[H_0:\mu=5700\;\;\;\;\;\;\;\;\;\; H_1:\mu>5700\;\;\text{ (Claim)}\]

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Step 2:

Collect your data

\[n=36\]

\[\overline{x}=5950\]

\[\sigma=659\]

\[\alpha=0.05\]

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Step 3: 

Calculate the P-value (you can use the table or the Hypothesis Calculator!)

\[P=0.9885\]

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Step 4:

Analysis

Since \(P>1-\alpha=0.95\) we reject \(H_0\) and hence we have enough evidence to support our claim.