A cream with alpha-hydroxy acid, advertises that it can reduce wrinkles and improve the skin. In a study published in Archives of Dermatology (June 1996), 49 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 any improvement in the condition of her skin. The results for the 49 women (where I = improved skin and N = no improvement) were: 32 I’s and 17 N’s. (a) Find a 95% confidence interval for p, the true population proportion of middle-aged women with improved skin after using this cream. Interpret the interval. (b) What assumptions are required for the confidence interval of part (a) to be statistically valid? (c) Are the assumptions for part (b) reasonably satisfied? Explain.
A cream with alpha-hydroxy acid, advertises that it can reduce wrinkles and improve the skin. In a study published in Archives of Dermatology (June 1996), 49 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 any improvement in the condition of her skin. The results for the 49 women (where I = improved skin and N = no improvement) were: 32 I’s and 17 N’s.
(a) Find a 95% confidence interval for p, the true population proportion of middle-aged women with improved skin after using this cream. Interpret the interval.
(b) What assumptions are required for the confidence interval of part (a) to be statistically valid?
(c) Are the assumptions for part (b) reasonably satisfied? Explain.
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