3. By statistics, faculty with rank of assistant professor (AP) finishing their

Question

3. By statistics, faculty with rank of assistant professor (AP) finishing their 2nd year of employment at a higher education institution in Ontario earn an average of $ 75,360 per year with a standard deviation of $2,800. In an attempt to verify this salary level, a random sample of 40 APs with 2 years of experiment was selected from a personnel database for all higher education institutions in Ontario. [6] a) Describe the sampling distribution of the sample mean X of the average of these 40 APs. [10] b) Within what limits would you expect the sample mean to fall with probability 0.95? [3] c) If the random sample actually produced a sample mean X = $72, 000, would you consider this rather unusual? What conclusion might you draw then?

Explanation / Answer

Mean is 75360 and s is 2800

a) Mean is 75360 and for the sample

The standard error is:

s/sqrt(N) = 2800/sqrt(40) = 442.72

b) for the confidence interval of 95%, the z value is 1.96

thus lower limit is mean - SE*z= 75360-1.96*442.72= 74492.27

upper limit is mean + SE * z= 75360 + 1.96*442.72= 76227.73

c) z for 72000 is (x-mean)/SE which is (7200-75360)/442.72=-153.96

this is very unusual because it lies more than 3 standard deviations (i.e z = -3) away from the mean and doesn't lie in the above interval.

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