ass Assignment May 23 2018 the United States, the following information erence b

Question

ass Assignment May 23 2018 the United States, the following information erence between the yearly incomes of marketing managers in the East and West of was gathered. East West ni 40 1 72 (in $1,000) 278 (in $1,000) s1 -6 (in $1,000) s2 8 (in $1,000) a. Develop an interval estimate for the difference between the average yearly incomes of the marketing managers in the East and West. Use a -0.05. At 95% confidence, use the p-value approach and test to determine ifthe average yearly income of marketing managers in the East is significantly different from the West. b

Explanation / Answer

Ans:

a)Assume equal populations variances.

pooled standard deviation=sqrt((40-1)*6^2+(45-1)*8^2)/(40+45-2))=7.13

standard error=7.13*sqrt((1/40)+(1/45))=1.549

df=40+45-2=83

critical t value=tinv(0.05,83)=1.989

95% confidence interval for difference in means

=(72-78)+/-1.989*1.549

=-6+/-3.08

=(-9.08, -2.92)

As,above interval does not include 0 within its limits,so we can conclude that the average yearly income of marketing managers in the East is significantly different from the West.

b)

Test statistic:

t=(72-78)/1.549

t=-3.87

p-value=tdist(3.87,83,2)=0.0002

As,p-value<0.05,we reject the null hypothesis and we can conclude that  the average yearly income of marketing managers in the East is significantly different from the West.

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