A new cream that advertises that it can reduce wrinkles and improve skin was sub

Question

A new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of 45 women over the age of 50 used the new cream for 6 months. Of those 45 women, 31 of them reported skin improvement (as 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 alpha = 0.05. test statistics z = rejection region z > The final conclusion 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.

Explanation / Answer

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 =    0.688888889      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.073029674      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    1.217161239   [ANSWER, TEST STATISTIC]

**************************************

As this is right tailed, 0.05 level,

rejection region: z > 1.645 [ANSWER]

***************************************  
          
As z < 1.645, we   FAIL TO REJECT THE NULL HYPOTHESIS. [OPTION A, ANSWER]      

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.