The following data represents the running time of films produced by 2 motion pic

Question

The following data represents the running time of films produced by 2 motion picture companies.   Assume these are independent samples:

Company             Time (in minutes)                                                    

Company 1         102     86        98        109     92

Company 2         81        165     97        134     92        87        114

Test the null hypothesis that the average running time of the films produced by company 2 exceeds the average running time of films produced by company 1 by an amount of 10 minutes. Test against the null hypothesis of a one sided alternative that the difference is more than 10 minutes.

a.) Perform the Hypothesis test at alpha = .1

b.) Determine the confidence interval for the difference between the means at 90% CI

Explanation / Answer

a)

H0: 2 – 1 = 10

H1: 2 – 1 > 10

Assuming population variances are equal, we would have to calculate pooled-variance t-Test keeping company 2 as population 1 and company 1 as population 2

Sp^2= (n1-1)S1^2+(n2-1)S2^2/(n1-1)+(n2-1)

         = 6*913.33+4*78.8/6+4

         = 5480+315.2/10

         =579.52

tSTAT=(X1-X2)-(µ1-µ2)/Sp^2(1/n1+1/n2)

       =(110-97.4)-0/579.52(1/7+1/5)

       =0.8939

tCRIT is 1.37 and hence cannot reject the null hypothesis.

Confidence interval:-

(X1-X2)+-ta/2*Sp^2(1/n1+1/n2)

12.6+/-1.81* 0.34

b)

LCL=12.6-0.6154=11.9846

UCL=12.6+0.6154=13.2154

Company 1 Company 2 102 81 86 165 98 97 109 134 92 92 87 114 97.4 110 Mean 8.876936408 30.22140522 SD

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