statistics hypotheses testing

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Question description

1.  A researcher at the American Medical Association wrote a report recently that stated the average annual salary of psychiatrists is $189,121 [img width="96" height="22" src="file:///C:/Users/Markia/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif" v:shapes="_x0000_i1025">σ = 26975).  A group of hospital administrators in the Northeast randomly sampled 64 psychiatrists (n = 64) and found an average annual salary of $198,630 [img width="98" height="22" src="file:///C:/Users/Markia/AppData/Local/Temp/msohtmlclip1/01/clip_image004.gif" v:shapes="_x0000_i1025">

a.  (14 points) Conduct a hypothesis test to determine if the administrators are correct, that the average salary is significantly higher than reported by the researcher. Test using the traditional method using α = 0.05.

b.  (3 points) What is the p-value for the test value found in part a (assuming the same alternative hypothesis). 

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