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Hog95 Hog95
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Posts: 2985
7 years ago
A psychologist obtained recordings of election-night acceptance speeches of seven newly elected representatives to the U.S. Congress and counted the number of minutes devoted to urban problems in these speeches. The four of these representatives from rural districts devoted 5, 0, 3, and 4 minutes to urban problems, and the three representatives from urban districts devoted 11, 11, and 14 minutes to urban problems. Using the .05 significance level, did the amount of time devoted to urban problems in the acceptance speech differ according to the type of district the representative represented?
a.   Use the five steps of hypothesis testing.
b.   Sketch the distributions involved.
c.   Figure the effect size.
d.   Explain the logic of what you did to a person who is familiar with the t test for a single sample, but who is unfamiliar with the t test for independent means. Be sure you explain how this problem differs from a t test for a single sample. Your answer should consist mainly of a thorough explanation of the characteristics of the comparison distribution and the logic of all the steps of figuring you did to determine those characteristics. 
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padrepadre
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7 years ago
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A)   Rural:   N = 4; df = 3; M = 3; S2 = 4.67
Urban:   N = 3; df = 2; M = 12; S2 = 3
dftotal = 5; S2pooled = [(3/5)(4.67)] + [(2/5)(3)] = 2.80 + 1.20 = 4
S2M1 = 4/4 = 1; S2M2 = 4/3 = 1.33
S2difference = 1 + 1.33 = 2.33; Sdifference = 1.53
t needed (df = 5, p < .05, two-tailed) = ±2.571
t = (–3 – 12)/1.53 = –5.88
Reject the null hypothesis.

C)   Estimated d = (–3 – 12)/2 = –4.5
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Thank you so much for the reply. Your answer makes a lot of sense.
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