A random sample of 80 couples in a particular city are observed to test whether

Question

A random sample of 80 couples in a particular city are observed to test whether husbands watch less TV per week than their wives.

(a) Explain briefly why the data in this situation would be considered paired and not independent.

(b) Using a sample mean difference (husband’s minus wife’s) of 1.2 hours and sample standard deviation of 7, conduct the appropriate test at the .05 level of significance. Report the hypotheses, your test statistic, and conclusion.

(c) If the mean difference for all couples is 2.0 hours, what is the power of the test in part (b)? For this part, you may treat 7 as the population standard deviation.

Explanation / Answer

a) cause at different household viewing of TV time will be different for both husband and wives

b)here std error =std deviation/(n)1/2 =0.7826

test stat t=(X-mean)/std error =(-1.2)/0.7826 =-1.5335

for above p value =0.0646

as p value is higher then 0.05 level we can not accept that  husbands watch less TV per week than their wives.

c) here true mean =-2 hours

for 0.056 level ; z=-1.6449

hence powwer of the test =P(Z<(-1.6449-(-2-(-1.2))*(80)1/2)/7) =P(Z<-1.6449+1.0222)=P(Z<-0.6227)=0.2668

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