Question

A university health center tracks the number of flu-related visits during each month of the fall semester. The center director wonders whether students come down with the flu more often around mid-October)and mid December. Can these data shed any light on this issue?

Flu-Related Visits to the University Health Center

(by months)

September	October	November	December
20	48	27	56

      Is there any significant difference among the flu-related visits during the fall semester? Use an α level of .05 to test the appropriate hypothesis,

Answer 1

Solution:

Here, we have to use chi square test for goodness of fit.

Null hypothesis: H0: There is no any significant difference among the flu-related visits during the fall semester.   

Alternative hypothesis: Ha: There is a significant difference among the flu-related visits during the fall semester.   

We are given level of significance = α = 0.05

We are given

Number of categories = N = 4

Degrees of freedom = df = N - 1 = 3

α = 0.05

Critical value = 7.81472776

(by using Chi square table or excel)

Test statistic formula is given as below:

Chi square = ∑[(O – E)^2/E]

Where, O is observed frequencies and E is expected frequencies.

Calculation tables for test statistic are given as below:

Month	O	E	(O - E)^2/E
September	20	37.75	8.34602649
October	48	37.75	2.78311258
November	27	37.75	3.06125828
December	56	37.75	8.82284768
Total	151	151	23.013245

Test Statistic = Chi square = ∑[(O – E)^2/E] = 23.013245

χ2 = 23.013245

P-value = 0.00004

(By using Chi square table or excel)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that there is a significant difference among the flu-related visits during the fall semester.