QUESTION 7 The 2000 American Academy of Physician Assistants (AAPA) survey of th

Question

QUESTION 7 The 2000 American Academy of Physician Assistants (AAPA) survey of the population of 1434 physicians assistants who were working full-time after graduating in 1999 reported a mean annual income of $58000 and standard deviation of $11000. Suppose that AAPA had randomly sampled 100 physicians assistants instead of collecting data for all 1434 of them. We would consider a random sample of 100 physicians assistants to be unusual if their average salary was in the top 2.5% or the bottom 2.5%. What average salary would 100 physicians assistants have to have in order to be considered unusual?

Explanation / Answer

z- scores such that area to its left or right is 2.5% are z1 = -1.96 and z2 = 1.96

x1 = + z1 * = 58000 - 1.96 * 11000 = $36440

x2 = + z2 * = 58000 + 1.96 * 11000 = $79560

The unusual average salaries are those less than $36440 or more than $79560.

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