Question

A new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of 54 women over the age of 50 used the new cream for 6 months. Of those 54 women, 37 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 α=0.05.

Answer 1

Null hypothesis     

H0: P= 0.40
              
Alternative hypothesis  

H1: P > 0.40
              
We have for given example,              
Population proportion value is =0.4          
x=37          
              
n=54          
Level of significance =   0.05          
Estimate for sample proportion = 0.6852      
              
Z test statistic formula for proportion

P value is approximately 0 ..........................by using Excel command =1-NORMSDIST(4.28) or by using Z table.

P value is < 0.05

Therefore, we reject H0.

Conclusion: We have sufficient evidence to say that, the cream will improve the skin of more than 40% of women over the age of 50