A. The university system boasts that over 50% of its administrators have master’

Question

A. The university system boasts that over 50% of its administrators have master’s degrees. Provide the formal null and alternative hypotheses for a test of this question. Is this a one or two-tailed hypothesis?

B. Do you have a large enough sample to conduct a hypothesis test? Explain with a calculation why or why not.

C. If your answer to part “B” is yes, then conduct this hypothesis test based on the 95% significance level. Do you reject or fail to reject your null hypothesis? Why?

Salary ($) Master's Degree (1 = Yes) 100000 1 76000 0 97200 0 90700 1 101800 1 88700 0 84200 0 97600 1 99400 0 84300 0 78700 0 102700 1 103400 0 83800 0 111300 1 94700 0 69200 0 85400 1 61500 0 108800 1

Explanation / Answer

a)
This is one tailed test i.e. right tailed test.

b)
Sample is large enough to conduct the hypothesis test

Now at this point we want to check whether the sample size is large enough so that we can use the one-proportion z-test.
Check the conditions below now. 1) np 5, and 2) n(1p) 5

here, np = 8 and n(1-p) = 12
Both condition satisfied

c)

Below are the null and alternate hypothesis

H0: p = 0.5 and H1: p > 0.5

Test statistics, z = (0.4 - 0.5)/0.1095 = -0.9132

p-value = 0.8194

Fail to reject null hypothesis as p-value is greater than the significance level.

n 20 p 0.4 z-value of 95% CI 1.959963985 SE = sqrt(p*(1-p)/n) 0.109544512

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