Question

An article in the Washington Post stated that nearly 45 percent of all Americans take a daily medication. A random sample of n = 82 people in Georgia found 31 who take a daily medication.
Use this information to test the hypotheses:
H0:p=.45H0:p=.45
Ha:p≠.45Ha:p≠.45
where p represents the population proportion of Georgians who take a daily medication.

(a) What is the value of the sample proportion of Georgians who take a daily medication?
p^=p^=

(b) What is the zz test-statistic for this test?  

(c) What is the p-value of the test?  

A new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of 6161 women over the age of 50 used the new cream for 6 months. Of those 6161 women, 5050 of them reported skin improvement(as judged by a dermatologist). Is this evidence that the cream will improve the skin of more than 4040% of women over the age of 50? Test using α=0.05α=0.05.

(a) p-value =

Answer 1

Solution :

1) Given :

n=82, x=31, p0=0.45

Hypothesis :

Where p represents the population proportion

a) Sample proportion is

=31/82

= 0.378

b) z-test statistic :

By using One sample proportion z-test,

The z-test statistic is computed as follows:

c) P-value is calculated by using excel command "2*NORM.S.DIST(-1.31,TRUE)"

P-value = 0.1903

2) Given:

n=61, x=50, p0=0.40

Hypothesis :

Sample proportion is

=59/61

=0.8197

By using One sample proportion z-test,

z-test statistic

a) P-value is calculated by using excel command "NORM.S.DIST(-0.694,TRUE)"

P-value =1.08576E-11 i. e. P-value is <0.00001

i. e. P-value=0

Conclusion :

P-value <0.05, we reject H0

Therefore, This is the evidence that cream will improve the skin more than 40% of women over the age of 50.