Question 394805: Do students at various universities differ in how sociable they are? Twenty-five
students were randomly selected from each of three universities in a region and
were asked to report on the amount of time they spent socializing each day with
other students. The result for University X was a mean of 5 hours and an estimated
population variance of 2 hours; for University Y,M = 4, S^2 = 1.5 ; and for University Z,M = 6, S^2 = 2.5
. What should you conclude? Use the .05 level.
(a) Use the steps of hypothesis testing, (b) figure the effect size for the study;
and (c) explain your answers to parts (a) and (b) to someone who has never had
a course in statistics.
Answer by jrfrunner(365)   (Show Source):
You can put this solution on YOUR website! Ho: Ux=Uy=Uz
Ha: not all are equal
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compute the sum squares for between groups x,y,z
SSB=sum(ni*(Xi-Xbar)^2) where ni=sample size for group i, Xi=sample average for group i, and Xbar=overall average.
ni=25 for each group, Xx=5,Xy=4,Xz=6, Xbar=5
SSB=25*(0^2+(-1)^2+1^2)=50
degrees of freedom= k-1=3-1=2, k=number of groups
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Compute the sum squares for the error
SSE=sum((ni-1)*Si^2)=24*(2+1.5+2.5)=144
degrees of freedom= k(ni-1)=3(25-1)=3*24=72, k=number of groups
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Compute Mean sum of squares for between groups and error
MSB=SSB/dof=50/2=25
MSE=SSE/dof=144/72=2
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compute F statistic= MSB/MSE=25/2=12.5
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determine the critical F value for alpha 0.05, num dof=2, denom dof=72
Fcritical= 3.12
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Since Fstatistic > Fcritical then reject Ho and conclude
The universities differ in their average time socializing
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