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View Controls Store Window Help 100% B, Wed 1 webwork2.uncc.edu MATHEMATICAL ASSOCIATION OF AMERICA Logged in as sva webwork / fal 2015-stat 1222-091/ practice exam 3/8 Practice Exam 3: Problem 8 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 68 women over the age of 50 used the new cream for 6 months. Of those 68 women, 35 of them reported skin im judged by a dermatologist). Is this evidence that the cream will improve the skin of more than 60% of women over the age of 50? Test using 0.05 provement(as test statistics z = rejection region z > The final conclustion is A There is not sufficient evidence to reject the null hypothesis that p = 0.6 That is, there is not sufficient evidence to reject that the cream can improve the skin of more than 60% of women over 50. B. We can reject the null hypothesis that p = 0.6 and accept that p > 0.6. That is, the cream can improve the skin of more than 60% of women over 50. Note: You can earn partial credit on this problem. Preview My Answers Submit Answers You have attempted this problem 5 times Your overall recorded score is 33%. You have unlimited attempts remainin

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.6
Ha:   p   >   0.6
As we see, the hypothesized po =   0.6      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.514705882      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.059408853      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -1.435713937   [ANSWER, TEST STATISTIC]

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As alpha = 0.05 and right tailed, the rejection region is z > 1.645. [ANSWER]

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As z < 1.645, then:

OPTION A: There is not sufficient evidence to reject the null hypothesis that p = 0.6. [ANSWER]