Question

Salary ($)	Master's Degree (1 = Yes)
100000	1
76000	0
97200	1
90700	1
101800	1
88700	0
84200	0
97600	1
87200	0
84300	0
78700	0
102700	1
103400	0
83800	0
111300	1
81500	1
72200	0
85400	1
61500	0
99900	1

1. The university system boasts that over 70% 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?
2. Do you have a large enough sample to conduct the correct hypothesis test? Explain with a calculation why or why not.
3. If your answer to part “h” is yes, then conduct this hypothesis test based on the 95% significance level. Do you reject or fail to reject your null hypothesis? Why?

Answer 1

n = 20

x = 10

= x/n

= 10/20

= 0.5

H0: p = 0.7

H1: p> 0.7

This is a one-way hypothesis.

Since x = 10 >5 and n-x = 10 > 5 i.e. we have all the conditions satisfied to conduct the test.

Hypothesis Test:

p-value = 0.9745 > 0.05 i.e. we fail to reject null hypothesis.

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