Question

Skitzy Schizophrenic at the American Medical Association wrote a report recently that stated the average annual salary of psychiatrists is $189,121  with a population standard deviation of $26,975 (σ = 26975).  A group of hospital administrators in the Northeast randomly sampled 64 psychiatrists (n = 64) and found an average annual salary of $196,430(X=196430 ).  The group of administrators claims that the average annual salary in their region is actually higher than what Skitzy reported.

Conduct a hypothesis test to determine if the administrators are correct, that the average salary is significantly higher than reported by Skitzy. Test using the traditional method using α = 0.05.

Make sure you provide all 5 steps to your hypothesis test.

Answer 1

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1. Hypothesis:

Ho: Mu <= 189,121

2.

Ha: Mu > 189,121

3.

Significance level is alpha = .05

4. test-statistic = (Xbar - Mu)/(Stdev/sqrt(n)) = (196430-189121)/(26975/sqrt(64)) = 2.17

p-value = P(|t|>2.17 at df = n-1=63) = .017

5. Since p-value < alpha = .05, we conclude that null hypothesis stands rejected and that the claim that the average annual salary in their region is actually higher than what Skitzy reported is correct