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 (elther paper or electronic). The sample of 21 traditional paper-coupon clippers had a mean age of 421 with a standard deviation of 5.6. The sample of 35 e-coupon users had a mean age of 36.7 years with a standard deviation of 9.5. Assume the population standard deviations are not the same. Using a significance level of 0.01, 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. Required: a. What are the null and alternate hypotheses? O Ho: Pe-coupon traditional H: He-coupon O Ho: He-coupon * Ptraditional H: Pe-coupon Ptraditional O Ho: Pe-coupon * Ptraditional H: Pe-coupon Ptraditional b. Compute the test statistic. (Negative values should be Indicated by a minus sign. Round your answers to 2 decimal places.) Test statistic Ptraditional c. Compute the p-value. NOTE: P-value calculators are available through online search. (Round your answer to 4 decimal places.) p-value d. What is your decision regarding the null hypothesis? Reject the Ho O Fall to reject the He e. Interpret the result.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 10CYU

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Transcribed Image Text: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 (elther paper or electronic). The sample of 21 traditional paper-coupon clippers had a mean age of 42.1 with a standard deviation of 5.6. The sample of 35 e-coupon users had a mean age of 36.7 years with a standard deviation of 9.5. Assume the population standard deviations are not the same. Using a significance level of 0.01, 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. Required: a. What are the null and alternate hypotheses? O Ho: Pe-coupon = Htraditional H₁: He-coupon # traditional O Ho: He-coupon # traditional H₁: He-coupon traditional O Ho: Pe-coupon #Ptraditional H₁: He-coupon * Ptraditional b. Compute the test statistic. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) Test statistic c. Compute the p-value. NOTE: P-value calculators are available through online search. (Round your answer to 4 decimal places.) p-value d. What is your decision regarding the null hypothesis? O Reject the He O Fall to reject the He e. Interpret the result.

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