Exercise 11-28 (LO11-2) Businesses such as General Mills, Kellogg\'s, and Betty
ID: 3360931 • Letter: E
Question
Exercise 11-28 (LO11-2) Businesses such as General Mills, Kellogg's, and Betty Crocker regularly use coupons to build brand allegiance and stimulate sales. Marketers believe that the users of paper coupons are different from the users of e-coupons accessed through the Internet One survey recorded the age of each person who redeemed a coupon along with the type of coupon (either paper or electronic). The sample of 26 traditional paper-coupon clippers users had a mean age of 33.1 years with a standard deviation of 9.5. Assume the population standard deviations are not the same. had a mean age of 39.1 with a standard deviation of 71. The sample of 35 e-coupon 10 awarded Using a significance level of 0.025, test the hypothesis of no difference in the mean ages of the two groups of coupon clients. Hint For the calculations, assume e-coupon as the first sample. ored a. Find the degrees of freedom for unequal variance test (Round down answer to nearest whole number) 60 0 b. State the decision rule for 0025 significance level: Ho, -eoupoa-utraditional ; H-he-coupon #Her aditional" (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.) c. Compute the value of the test statistic.(Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) 2.71Explanation / Answer
Answer to part a)
The formula of degree of freedom is :
df = (s1^2/n1 + s2^2/n2)^2 / [(1/(n1-1) * (s1^2/n1)^2 + (1/(n2-1)) * (s2^2/n2)^2]
.On plugging the values we get:
df = ((7.1^2/26)+(9.5^2/35))^2 / (((1/25)*(7.1^2/26)^2)+ (1/34)*(9.5^2/35)^2)
df = 58.99279 ~ 59
.
Answer to part b)
The t critical value can be obtained using the excel formula
=T.INV.2T(0.025,60)
we get T critical = -2.2990 and +2.2990
Thus reject Ho , when t < -2.2990 , and t > +2.2990
.
Answer to part c)
The formula of Test statistic is as follows:
t = (x1 bar - x2 bar) / sqrt( s1^2/n1 + s2^2/n2)
.
On plugging the values we get
t = (39.1 -33.1) / sqrt((7.1^2/26)+(9.5^2/35))
t = 2.8230 ~ 2.82
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