Homework11: Problem 9 Previous Problem List Next (1 point) A new cream that adve

Question

Homework11: Problem 9 Previous Problem List Next (1 point) A new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of 40 women over the age of 50 used the new cream for 6 months. Of those 40 women, 32 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:20 = (c) The decision and final conclusion are O A We can reject the null hypothesis that p s 0.5 and support the claim that p > 0.5. That is, the cream can improve the skin of more than 50% of women over 50. O B. There is not sufficient evidence to reject the null hypothesis that p s 0.5. That is, we cannot support the claim that the cream can improve the skin of more than 50% of women over 50. Note: You can earn partial credit on this problem.

Explanation / Answer

The statistical software output for this problem is:

One sample proportion summary hypothesis test:
p : Proportion of successes
H0 : p = 0.5
HA : p > 0.5

Hypothesis test results:

Hence,

a) Test statistic = 3.7947

b) Critical Value = 2.33

c) Option A is correct.

Proportion Count Total Sample Prop. Std. Err. Z-Stat P-value p 32 40 0.8 0.079056942 3.7947332 <0.0001

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