Based on a sample of N=20, the mean price of new homes in PA is $280K and the st

Question

Based on a sample of N=20, the mean price of new homes in PA is $280K and the standard deviation is $179K. The national average home price is $265K. You must use the sample standard deviation given for PA of $179K. Suppose you want to test whether homes in PA are higher than the national average.

Part A: Calculate the test statistic for the sample mean of the PA home prices.

Part B: Using the appropriate Table (t table) find the Critical Value for a = 0.05 to calculate the exact p-value for the value of test-statistic.

Part C: Can you reject the Null Hypothesis at a significance level of a = 0.05?

Explanation / Answer

Set Up Hypothesis
Null, H0:homes in PA are not as greater as national average U<265
Alternate,homes in PA are higher than the national average H1: U>265
Test Statistic
Population Mean(U)=265
Sample X(Mean)=280
Standard Deviation(S.D)=179
Number (n)=20
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =280-265/(179/Sqrt(20))
| to | =0.375
Critical Value
The Value of |t | with n-1 = 19 d.f is 1.729
We got |to| =0.375 & | t | =1.729
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Right Tail - Ha : ( P > 0.3748 ) = 0.35599
Hence Value of P0.05 < 0.35599,Here We Do not Reject Ho

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