Question

A study is run in which 900 individuals are sampled and each is classified as to whether they had contracted the flu during the last year and whether they had been inoculated for the flu. The research question is whether inoculation status and contracting the flu are associated and what is the magnitude of the association.

	flu
Inoculation Status	flu	no flu
inoculated	150	200
Not Inoculated	300	250

Do a chi-square test to see if there is an association between inoculation and getting the flu.

1. What would be the null and alternate hypothesis for this question?

2. if the p-value is 0.006, Statement of conclusion both as “reject or fail to reject the null hypothesis” and as a verbal statement explaining the meaning of that conclusion in this context.

Answer 1

(A) We want to test for the association between inoculation and getting the flu. We will be using the chi-square test statistic to check whether the null hypothesis is rejected or retained.

So, for alternate hypothesis, we assume that there is some  association between inoculation and getting the flu and for null hypothesis, we assume that there is no  association between inoculation and getting the flu.

Null hypothesis:- There is no  association between inoculation and getting the flu.

Alternate hypothesis:- There is a significant  association between inoculation and getting the flu.

(B) We know that when the p value is greater than significance level, then say that we failed to reject the null hypothesis and when the p value is less than significance level, we say that we can reject the null hypothesis.

In this case, we p value = 0.006, which is less than significance level of 0.01 or 0.05. So, we can say that the result is significant as the p value is less than significance level. Thus, we can reject the null hypothesis and we can conclude that there is a significant association between inoculation and getting the flu.