A new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of $46$ women over the age of 50 used the new cream for 6 months. Of those $46$ women, $36$ 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 $\alpha = 0.05$.

(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 $p = 0.4$. That is, there is not sufficient evidence to reject that the cream can improve the skin of more than $40$% of women over 50.
B. 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.