Researchers are conducting a study investigating the relationship between caffeinated coffee consumption and risk of depression. The researchers collected data listed below:

Caffeinated coffee

Consumption

Less then one cup a day More than one cup a day

Has depression 104 156

Patient status Doesnt have

depression 1776 3034

Our goal is to test for independence between these two variables using an alpha value of 0.01.

a. Identify the null and alternative hypothesis for this test of independence.

b. What is the test statistic for this test? (Round to three decimal places)

c. What is the correct number of degrees of freedom for the critical region?

d. What is the value that defines the critical region? (Round to three decimal places)

e. What is the p-value for this test?

p > 0.10

0.05 < p < 0.10

0.025 < p < 0.05

p < 0.005

What is the conclusion for this test? Is there an association between caffeinated coffee consumption and depression on the basis of this data?