new cream that advertises that it can reduce wrinkles and improve skin was subje

Question

new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of 42 women over the age of 50 used the new cream for 6 months. Of those 42 women, 35 of them reported skin improvement(as judged by a dermatologist). Is this evidence that the cream will improve the skin of more than 50% of women over the age of 50? Test using =0.01.

(a) Test statistic: z=

(b) Critical Value: z=

(c) The final conclusion is

A. There is not sufficient evidence to reject the null hypothesis that p=0.5. That is, there is not sufficient evidence to reject that the cream can improve the skin of more than 50% of women over 50.
B. We can reject the null hypothesis that p=0.5 and accept that p>0.5. That is, the cream can improve the skin of more than 50% of women over 50.

Explanation / Answer

a) sample Proportion = 35/42 = 0.83

Z = (0.83-0.50)/Sqrt(0.50*0.50/42) = 4.277

b) Critical value at 0.01 level is 2.326

c) Option B is Correct because test statistic is greater than 2.326

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