Question

While this question is a multiple choice question, I would like to know the formula/math behind the multiple choices and how to find the answers. Any help would be appreciated! Thank you!

According to the American Veterinary Medical Association, 30.4% of households in the US own cats. Three research teams wanted to test whether this percentage was different in different states:

H0:π=0.304

Ha:π≠0.304

where π is the proportion of all households in the state that own cats.

a) The team studying New York finds a p-value of .002.
What can you say about the 95% and 99% confidence intervals for ππ?

A. Both the 95% and 99% confidence intervals will contain 0.304.
B. Neither the 95% nor the 99% confidence interval will contain 0.304.
C. The 95% interval will contain 0.304, but the 99% interval will not.
D. The 99% interval will contain 0.304, but the 95% interval will not.

b) The team studying California finds a p-value of .03. What can you say about the 95% and 99% confidence intervals for ππ?

A. Both the 95% and 99% confidence intervals will contain 0.304.
B. The 99% interval will contain 0.304, but the 95% interval will not.
C. Neither the 95% nor the 99% confidence interval will contain 0.304.
D. The 95% interval will contain 0.304, but the 99% interval will not.

c) The team studying Wisconsin finds a p-value of .07. What can you say about the 95% and 99% confidence intervals for ππ?

A. The 99% interval will contain 0.304, but the 95% interval will not.
B. Both the 95% and 99% confidence intervals will contain 0.304.
C. Neither the 95% nor the 99% confidence interval will contain 0.304.
D. The 95% interval will contain 0.304, but the 99% interval will not.

Answer 1