Question

1. Below there is information for a 1 sample proportion hypothesis test:

H0:P= 0.75

HA:P> 0.75

α=0.01

1. 1. What is the smallest value of the test statistic that would provide enough evidence to reject the null hypothesis?
2. 2. If the sample size is 50, what is the value of σp?
3. 3. If the test statistic is 2 (sample size is still 50), what is the value of p?

Answer 1

Solution(a)
Given in the question
Null hypothesis H0: P = 0.75
Alternate hypothesis Ha: P > 0.75
alpha = 0.01
Solution(a)
Here we will use one proportion Z test and this is the right-tailed test so at alpha = 0.01, from Z table we found Zcritical value is 2.33
So If the test stat value is greater than 2.33 than we will reject the null hypothesis else we will not reject the null hypothesis. So Smallest value of test statistic 2.33 to reject the null hypothesis.
Solution(b)
Here Given that Sample size n = 50
So p can be calculated as
p = sqrt(P*(1-P)/50) = sqrt(0.75*(1-0.75)/50) = sqrt(0.75*0.25/50) = 0.0612
Solution(c)
Given Test stat = 2
Sample size = 50,
p = 0.06
So Test stat value can be calculated as
Test stat = (p-P)/p
2 = (p - 0.75)/0.0612
p = 0.8725