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Statistics for Business and Economics | 12th Edition | ISBN: 9780321826237 | Authors: James T. McClave, P. George Benson, Terry T Sincich
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Effectiveness of skin cream. Pond’s Age-Defying Complex, a

Chapter 7, Problem 77E

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QUESTION:

Problem 77E

Effectiveness of skin cream. Pond’s Age-Defying Complex, a cream with alpha hydroxy acid, advertised that it could reduce wrinkles and improve the skin. In a study published in Archives of Dermatology (June 1996), 33 middle-aged women used a cream with alpha hydroxy acid for 22 weeks. At the end of the study period, a dermatologist judged whether each woman exhibited skin improvement. The results for the 33 women (where I = improved skin and N = no improvement) are listed in the next table. [Note: Pond’s recently discontinued the production of this cream product, replacing it with Age-Defying Towlettes.]

a. Do the data provide sufficient evidence to conclude that the cream improved the skin of more than 60% of middle-aged women? Test using = .05.

b. Find and interpret the p-value of the test.

Questions & Answers

QUESTION:

Problem 77E

Effectiveness of skin cream. Pond’s Age-Defying Complex, a cream with alpha hydroxy acid, advertised that it could reduce wrinkles and improve the skin. In a study published in Archives of Dermatology (June 1996), 33 middle-aged women used a cream with alpha hydroxy acid for 22 weeks. At the end of the study period, a dermatologist judged whether each woman exhibited skin improvement. The results for the 33 women (where I = improved skin and N = no improvement) are listed in the next table. [Note: Pond’s recently discontinued the production of this cream product, replacing it with Age-Defying Towlettes.]

a. Do the data provide sufficient evidence to conclude that the cream improved the skin of more than 60% of middle-aged women? Test using = .05.

b. Find and interpret the p-value of the test.

ANSWER:

Solution 77E

Step1 of 3:

Let us consider a proportion ‘p’ it presents the proportion of middle-aged women who exhibit skin improvement after using the cream. Also, we have x = 24 and n = 33.

Here our goal is:

a). We need to check whether the data provide sufficient evidence to conclude that the cream improved the skin of more than 60% of middle aged women. With level of significance.

b). We need to find and interpret the p-value of the test.

I

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N

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N

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