Question

1. Salary ($)	Master's Degree (1 = Yes)
   61,500	0
   69,200	0
   76,000	0
   78,700	0
   81,500	0
   83,800	0
   84,200	0
   84,300	0
   85,400	1
   87,200	0
   88,700	0
   90,700	1
   97,200	0
   97,600	1
   99,900	1
   100,000	1
   101,800	1
   102,700	1
   103,400	0
   111,300	1

   1. a. The university system boasts that over 60% 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. b.Do you have a large enough sample to conduct the correct hypothesis test? Explain with a calculation why or why not.
   3. c. 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

A.

H₀: p 0.6

H₁: p > 0.6

This is a one-tailed hypothesis.

B.

n = 20

No. of people who have a master's degree, X = 8

= X/n

= 0.4

X= 8 5

n - X = 12 5

Hence, sampling distribution of can be approximated by normal distribution with mean = p = 0.4

and std. deviation = = 0.1095

C.

z = ( - p)/

= (0.4-0.6)/0.1095

= -1.826

p-value = 0.9661 > 0.05 i.e. H₀ can not be rejected.

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