Businesses such as General Mills, Kellogg\'s, and Betty Crocker regularly use co

Question

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 27 traditional paper-coupon clippers had a mean age of 32.8 with a standard deviation of 9.0. The sample of 35 e-coupon users had a mean age of 38.5 years with a standard deviation of 71. Assume the population standard deviations are not the same. Using a significance level of 0.050, 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. a. Find the degrees of freedom for unequal variance test. (Round down answer to nearest whole number) Degrees of freedom b. State the decision rule for 0.050 significance level: HO:Ho-coupon-Heraditional , Hi: e-coupon traditional. (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.) Reject HO if t

Explanation / Answer

(A) Degree of variance of unequal variance test will be calculated with help of following data

here we are noting e-coupon as 1 and traditional coupon as 2.

Sample standard deviation for e-coupon s1 = 7.1

Sample size for e - coupon n1 = 35

Sample standard deviation for traditional paper coupon s2 = 9.0

Sample size for tradition paper coupon n2 = 27

degree of freedom dF = (s12 /n1 + s22 /n2)2/[(s12 /n1)2/(n1 -1) + (s22 /n2)2/(n2-1)]

= (7.12/35 + 92/27)2/ [(7.12/35)2/34 + (92/27)2/26]  

= 48.4228 so we take dF = 49

(B) Here dF = 49 and alpha = 0.05

so decision rule is reject null hypothesis when

t < -2.01 or t > 2.01

(B) Here standard error of difference se0 = sqrt [s12/n1 + s22/n2] = sqrt [ 7.12/35 + 92/27]= 2.1072

Test statistic

t = (x1 - x2)/ se0 = (38.5 - 32.8)/2.1072 = 2.71

d. Here we will reject H0. There is significant difference in the mean age of the two groups of coupon details.

Related Questions

Navigate

• Browse (All)
• Browse B
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.