Question

A new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of 53 women over the age of 50 used the new cream for 6 months. Of those 53 women, 44 of them reported skin improvement (as judged by a dermatologist). Is this evidence that the cream will improve the skin of more than 50% of women over the age of 50? Test using α= 0.05.(a) Test statistic: = _____(b) Critical Value = _____(c) The final conclusion is:A. There is not sufficient evidence to reject the null hypothesis that p = 0.5. That is, there is not sufficient evidence to reject that the cream can improve the skin of more than 50% of women over 50.B. We can reject the null hypothesis that p = 0.5 and accept that p > 0.5. That is, the cream can improve the skin of more than 50% of women over 50.

Answer 1

Answer:

We reject H₀.  We accept Hₐ  (the cream can improve the the skin of more than 50%

Step-by-step explanation:

We have a proportion one tail test (right)

P₀  =  50 %     =  0,5

P  =  44/53     =  0.831

sample size  =  n   =  53

Confidence interval  =  0,95      α = 0.05    then   z(c)  =  1.64

1.-Hypothesis

H₀     null  hypothesis                     P₀  = 0.5

Hₐ   alternative hypothesis            P₀  > 0.5

2.-Compute  z(s)

z(s)  = ( P - P₀ ) / √P₀Q₀/n    ⇒    z(s)  = (0.831 - 0.5 )/√0.5*0.5/53

z(s)  = 0.3301/0.06

z(s)  = 5.5

3.-Compare  z(c)  and z(s)

z(s)  > z(c)         5.5  > 1.64

therefore   z(s) is in the rejection region  we reject  H₀ .  And accept Hₐ