A psychologist obtained recordings of election-night acceptance speeches of seve

Question

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? Part A (10 points) Use the five steps of hypothesis testing. Part B (5 points) Figure the effect size.

Explanation / Answer

Mrural = 3 Murban = 12

SSrural = 14 SSurban= 6

Mdifference = 6 SSdifference = 150

Difference = Urban – Rural

(a) Appropriate test for the given problem is t- test for equa;l variances as the ratio of variances is not more than 4. t - test is chosen over Z - test because population variance is not known.

(b) Null Hypothesis : H0 : There is no difference between time devoted to urban problems in the acceptance speech according to the type of district they represent. urban = rural

Alternative Hypothesis : H1 : There is significant difference between time devoted to urban problems in the acceptance speech according to the type of district they represent. urban rural

Test Statistic : t - test

pooled std. dev. sp =sqrt [(n1 -1) s12 +  (n2 -1) s22]/(n1 + n2 -2) =sqrt [(3*4.67 + 2 *3)/ (4+3-2)] = sqrt(4.00) = 2

so t = (Mrural - Murban) / sp sqrt(1/n1 + 1/n2 ) = (3 - 12)/ 2 * sqrt(1/4 + 1/3) = -5.89

for dF = 5 and alpha = 0.01

tcritical = -4.03

so here t < tcritical so we can reject the null hypothesis and can conclude that he amount of time devoted to urban problems in the acceptance speech differ according to the type of district the representative represented.

(D) T- test is more appropriate to other tests like Z- test, F - test or chi - square test because here sample data have very limited size and population proportions is unknown.

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