Question

A university investigation was conducted to determine whether women and men complete medical school in significantly different amounts of time, on the average. Two independent random samples were selected and the following summary information concerning times to completion of medical school computed. Perform the appropriate test of hypothesis, at level 0.05 to determine whether there is a significant difference in time to completion of medical school between women and men.

	Women	Men
Sample Size	90	100
Mean	8.4 years	8.5 years
Standard Deviation	0.6 years	0.5 years

Answer 1

ANSWER::

µ1 :- Average amount of time taken by women to complete medical school

µ2 :- Average amount of time taken by men to complete medical school

To Test :-
H0 :- µ1 = µ2
H1 :- µ1 ≠ µ2

Test Statistic :-


t = -1.2403

Test Criteria :-
Reject null hypothesis if | t | > t(α/2, DF)


DF = 173

Critical value t(α/2, DF) = t(0.05 /2, 173 ) = 1.974 ( From t table )

i.e t < - 1.974 Or t > 1.974

| t | > t(α/2, DF) = 1.2403 < 1.974
Result :- Fail to Reject Null Hypothesis

Decision based on P value
P - value = P ( t > 1.2403 ) = 0.2165
Reject null hypothesis if P value < α = 0.05 level of significance
P - value = 0.2165 > 0.05 ,hence we fail to reject null hypothesis
Conclusion :- Fail to Reject Null Hypothesis

There is insufficient evidence to support the claim that on average women and men complete medical school in different amount of time.

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