Question

For the following​ information, determine whether a normal sampling distribution can be​ used, where p is the population​ proportion,α is the level of​ significance, ModifyingAbove p with caretp is the sample​ proportion, and n is the sample size. If it can be​ used, test the claim. ​Claim:

p>0.29

α=0.08

Sample​ statistics:

ModifyingAbove p with caretpequals=0.36

n=375

Answer 1

Solution:
Null hypothesis H0: p<=0.29
Alternate hypothesis Ha: p>0.29
phat = 0.36
We will use normal sampling distribution as sample size is greater than 30
Ztest Stat = (0.36-0.29)/sqrt(0.29*0.71/375) = 2.99
From Z table we found p-value = 0.0014
at alpha = 0.08, we can reject the null hypothesis as p-value is less than alpha value(0.08<0.0014)
So we can reject the null hypothesis and We have significant evidence to support the alternative hypothesis.