Q1: A new cream that advertises that it can reduce wrinkles andimprove skin was subject to a recent study. A sample of 56 womenover the age of 50 used the new cream for 6 months. Of those 56women, 30 of them reported skin improvement(as judged by adermatologist). Is this evidence that the cream will improve theskin of more than 40% 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. We can reject the null hypothesis that p=0.4and accept that p>0.4. That is, the cream can improve the skinof more than 40% of women over 50.
B. There is not sufficient evidence to reject thenull hypothesis that p=0.4. That is, there is not sufficientevidence to reject that the cream can improve the skin of more than40% of women over 50.
Q2: A newspaper conducted a statewide survey concerning the 1998race for state senator. The newspaper took a SRS of n=1300registered voters and found that 670 would vote for the Republicancandidate. Let pp represent the proportion of registered voters inthe state who would vote for the Republican candidate.
We test
H0:p=.50
Ha:p>.50
(a) What is the z-statistic for this test?
(b) What is the P-value of the test?
