Question

A doctor would like to evaluate whether flu-frequency is different among patients of various ages. He groups his most recent 12 patients into four groups according to age (pediatric, young adult, older adult, senior), and counts the frequency of their flu-related visits. Below is his data. Test the hypothesis that flu frequency is different among pediatric, adult, older adult, and senior patients using an alpha level of .01.

Pediatric	Young adult	Older adult	Senior
6	2	4	7
4	1	0	9
5	0	0	12

  Find the critical value:

  Calculate the obtained statistic:

Answer 1

	Column 1	Column 2	Column 3	Column 4	Total
Row 1	6	2	4	7	19
Row 2	4	1	0	9	14
Row 3	5	0	0	12	17
Total	15	3	4	28	50

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

H_0: flu frequency is not different among pediatric, adult, older adult, and senior patients

H_a​: flu frequency is different among pediatric, adult, older adult, and senior patients

critical value: :

Based on the information provided, the significance level is α = 0.01 , the number of degrees of freedom is df=(3−1)×(4−1)=6,

critical value = 16.812

Test statistic:

So from the above calculations

Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore  flu frequency is not different among pediatric, adult, older adult, and senior patients   at the 0.01 significance level.