Question

Chi-Square: Sample Questions

1. A social worker wants to know if the rate of depressive episodes differs by the time of

year. Using the data collected by a large hospital, the social worker records the number

of first-time admissions for depression that occurred during the past 5 years. The social

worker divides the year into four seasons. The number of first-time admissions are as

follows:

Spring

495

Summer

503

Autumn

491

Winter

581

Conduct an appropriate statistical test using alpha = .05 to determine whether depressive

episodes differ by time of year.

use the 8 Steps of Hypothesis

Testing to answer

1)State your hypotheses: H0 and H1

2)Select the appropriate statistical test

3)Indicate whether test is directional or non-directional

4)Specify a, N, and df (if appropriate)

5) Do your calculations

6) Determine critical value(s) for test statistic

7) Make the appropriate decision based on Steps 5 & 6 to reject or fail to reject your null hypothesis

8) State conclusion (interpret results) in words

Answer 1

Here we want to test "Wether the rate of depressive episodes differs by the time of year or not "

1) So the null hypothesis ( H₀ ) and the alternative hypothesis ( H₁ ) is given by:

H₀ : the rate of depressive episodes is equal by the time of year.

H_a : the rate of depressive episodes differs by the time of year.

2) Here we need to use chi square goodness of fit test.

3) The test is directional because time is directional variable.

4) There are four groups. So N = 4 and df = N - 1 = 4 - 1 = 3

5) Let's use excel for calculation:

The formula used on the above excel sheet are as follows: