A new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of 70 women ove r the age of 50 used the new cream for 6 months. Of those 70 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 40% of women over the age of 50? Test using α=0.01.
1 answer:
Answer:
Yes , evidence shows that the cream will improve the skin of more than 40% of women over the age of 50 in 0.01 significance level.
Step-by-step explanation:
We need to make a hypothesis test.
Let p be the proportion of women who used cream report skin improvement.
: p=0.4
: p<0.4
To test the hypothesis, we need to calculate z-score of the sample mean and compare its probability with the significance level.
z= where
p(s) is the sample proportion of women reported improvement (0.5) p is the proportion assumed under null hypothesis. (0.4) N is the sample size (70) Putting the numbers:
z= ≈ 1.71
And P(z<1.71) ≈ 0.955. Since 0.955>0.01 we fail to reject the null hypothesis that the cream will improve the skin of more than 40% of women.
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