In order to estimate the difference between the yearly incom

In order to estimate the difference between the yearly incomes of marketing managers in the East and West of the United States, the following information was gathered East West n1=40 n2=45 _ _ x1=72 (in $1,000) x2=78 (in $1,000) s1=6 (in $1,000) s2= 8 (in $1,000)

Solution

Answer to the question)

In order to estimate the difference , the best way is to find the confidence interval of the difference of sample means as that gives us the range of the difference between the two sample means

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We got:

n1 =40

n2 = 45

x1 = 72

x2 = 78

s1 = 6

s2 = 8

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The formula of confidence interval is :

(x1-x2) - t * SE , (x1-x2) + t* SE

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where t = t critical value that depends on confidence level 0.95 & df = 6+8-2 = 12

we refer to the t table to get this value

t = 2.179

,

SE = sqrt(s1^2/n1 + s2^2/n2)

SE = sqrt((6^2/40)+(8^2/45))

SE = 1.5239

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On plugging the values we get:

(72-78) - 2.179 * 1.5239 , (72-78) + 2.179 * 1.5239

-8.179, -2.6794

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Conclusion : since both the values of confidence interval are negative this implies that the group 1 has smaller mean as compared to group 2