Question

A new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of 50 women over the age of 50 used the new cream for 6 months. Of those 50 women, 44 of them reported skin improvement(as judged by a dermatologist). Is this evidence that the cream will improve the skin of more than 40% of women over the age of 50? Test using α=0.01. (a) Test statistic: z= (b) Critical Value: z∗= (c) The final conclusion is A. We can reject the null hypothesis that p=0.4 and accept that p>0.4. That is, the cream can improve the skin of more than 40% of women over 50. B. There is not sufficient evidence to reject the null hypothesis that p=0.4. That is, there is not sufficient evidence to reject that the cream can improve the skin of more than 40% of women over 50.

Answer 1

Option A is right.

Explanation:

Given that a new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of 50 women over the age of 50 used the new cream for 6 months. Of those 50 women, 44 of them reported skin improvement(as judged by a dermatologist)

`H_0: p=0.40\\H_a: p >0.40`

(Right tailed test)

Sample size = 50

Std error of proportion =
`\sqrt{(pq)/(n) } \\=0.0693`

p difference=
`(44)/(50) -0.40\\=0.48`

Z statistic = p diff/std error = 6.928

p value <0.00001

Since p is less than alpha, reject null hypothesis.

A. We can reject the null hypothesis that p=0.4 and accept that p>0.4. That is, the cream can improve the skin of more than 40% of women over 50.