Gender: Randomly Chosen? A large community college district has 1000 teachers, o
ID: 3217647 • Letter: G
Question
Gender: Randomly Chosen? A large community college district has 1000 teachers, of whom 50% are men and 50% are women. In this district, administrators are promoted from among the teachers. There are currently 50 administrators, and 70% of these administrators are men. a. If administrators arc selected randomly from the faculty, what is the approximate probability that the percentage of male administrators v. will be 70% or more? b. If administrators arc selected randomly from the faculty, what is the approximate probability that the percentage of female administrators will be 30% or more? c. How arc part a and part b related? d. Do your answers suggest that it is reasonable to believe the claim that I the administrators have been selected randomly from the Answer yes or no, and explain your answer.Explanation / Answer
Solution:
Technical, this is an application of the hypergeometric dist., since we are "selecting" administrators
without replacement; but this can be reasonably approximated using the binomial.
a) standard error of p is
sqrt[(0.5)(1-0.5)/50]=0.0707.
A p of 0.70 is (0.70-0.50)/0.0707=2.829 std dev from expected, which has a probability. of 0.0023 from normal table
From part (a) and part (b), it can be observed that the number of female administrators in the sample depends on the number of male administrators in the sample so b) & c) same 0.0023
d) not reasonable to believe teachers selected randomly - a p of 0.0023 is stat sig and a rare event
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