The average salary for a random sample of 49 new (less than 3 years) professors

Question

The average salary for a random sample of 49 new (less than 3 years) professors in psychology graduate departments in 2012 was $92,000. The population, all professors with all years of experience in psychology graduate departments across the country, earned an average salary of $111,960, with a standard deviation of $40,295. Did the average salary of the new full psychology professors differ from that of all psychology professors as a whole? Conduct the appropriate statistical test to answer this question.

a. What are the hypotheses in formal statistical notation?

b. Draw the distribution/rejection region(s)/critical value(s).

c. Compute the test statistic and show where it falls on your distribution in part b.

d. Make decision & Communicate results.

Using the data from #3 above, compute the 95% confidence interval for new professors.

a. What is the confidence interval?

b. How would you use this confidence interval to conduct the hypothesis test that you did for #3? That is, describe how you would reach the same conclusion by using the confidence interval.

Explanation / Answer

average salary of $111,960, with a standard deviation of $40,295

random sample of 49 and mean 92,000

H0 : mu = 92000

H1 : mu =| 92000

the test stat is calculated as

t = (xbar- mean)/(sd/sqrt(n))

(92000 - 111960)/(40295/sqrt(49)) = -3.46

the critical region is for alpha = 0.05 , and df = n-1 = 48

as this is 2 tail test the value is +/- 2.010

as the t stat is greater than t critical , hence we reject the null hypothesis in favor of alternate hypothesis and conclude that the mean salary is different from 111960

Please note that we can answer only 4 subparts of a question at a time , as per the answering guidelines

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