A new cream that advertises that it can reduce wrinkles and

A new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of 41 women over the age of 50 used the new cream for 6 months. Of those 41 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 60% of women over the age of 50? Test using =0.05.

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 =    0.82      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.069282032      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    3.175426481      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.000748082      

significance level =    0.05      

As P < 0.05, we REJECT THE NULL HYPOTHESIS.      

Thus, there is sufficient evidence that the cream will improve the skin of more than 60% of women over the age of 50. [CONCLUSION]