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a) Set up the null and alternative hypotheses needed to determine whether there is a difference in the proportions of younger and older women who would purchase Heavenly if it were marketed. Determine the test statistic. b) Determine the p-value. c) Provide your conclusion in the context of this problem. Use alpha = 0.05. d) Calculate a 95 percent confidence interval for the difference between the proportions of younger and older women who would purchase Heavenly if it were marketed. Interpret this interval. Provide Lower Confidence Limit (LCL) and Upper Confidence Limit (UCL), explicitly.

a) Set up the null and alternative hypotheses needed to determine whether there is a difference in the proportions of younger and older women who would purchase Heavenly if it were marketed. Determine the test statistic. b) Determine the p-value. c) Provide your conclusion in the context of this problem. Use alpha = 0.05. d) Calculate a 95 percent confidence interval for the difference between the proportions of younger and older women who would purchase Heavenly if it were marketed. Interpret this interval. Provide Lower Confidence Limit (LCL) and Upper Confidence Limit (UCL), explicitly.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.3: Conditional Probability; Independent Events; Bayes' Theorem
Problem 82E
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a) Set up the null and alternative hypotheses needed to determine whether there is a difference in the proportions of younger and older women who would purchase Heavenly if it were marketed. Determine the test statistic.
b) Determine the p-value.
c) Provide your conclusion in the context of this problem. Use alpha = 0.05.
d) Calculate a 95 percent confidence interval for the difference between the proportions
of younger and older women who would purchase Heavenly if it were marketed. Interpret
this interval. Provide Lower Confidence Limit (LCL) and Upper Confidence Limit (UCL),
explicitly.

3. The Manelli Perfume Company recently developed a new fragrance that it plans to market under the name "Heavenly." A number of market studies indicate that Heavenly has very good market potential. The sales department at Manelli is particularly interested in whether there is a difference in the proportions of younger and older women who would purchase Heavenly if it were marketed. There are two independent populations, a population consisting of the younger women and a population consisting of the older women. Each sampled woman will be asked to smell Heavenly and indicate whether she likes the fragrance well enough to purchase a bottle. A random sample of 100 young women revealed 19 liked the Heavenly fragrance well enough to purchase it. Similarly, a sample of 200 older women revealed 62 liked the fragrance well enough to make a purchase.
Transcribed Image Text:3. The Manelli Perfume Company recently developed a new fragrance that it plans to market under the name "Heavenly." A number of market studies indicate that Heavenly has very good market potential. The sales department at Manelli is particularly interested in whether there is a difference in the proportions of younger and older women who would purchase Heavenly if it were marketed. There are two independent populations, a population consisting of the younger women and a population consisting of the older women. Each sampled woman will be asked to smell Heavenly and indicate whether she likes the fragrance well enough to purchase a bottle. A random sample of 100 young women revealed 19 liked the Heavenly fragrance well enough to purchase it. Similarly, a sample of 200 older women revealed 62 liked the fragrance well enough to make a purchase.
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