Question

The data below represents a sample of 22 people and how they voted on a referendum in a recent election. You are a social scientist who is interested in investigating age differences in voting patterns.

	Young folks	Older folks	Total
Voted No	5	4	9
Voted Yes	6	7	13
TOTAL	11	11	22

1. State the kind of statistical test you will perform (i.e., chi-square or an ANOVA).

HINT: Look at the types of variables available to you, which test is best suited for these types of variables with this many categories?

2. State the research and null hypotheses using words and symbols when applicable.

3. Report the degrees of freedom and the corresponding critical value for your test.

4. Compute the test statistic (i.e., chi-square or an ANOVA).

HINT: Make a computation table to keep track of your work.

5. Using your critical and obtained values, make a decision regarding your null hypothesis.

6. What conclusions can you draw about the voting behaviors of older and younger folks? Even if you don’t have enough information to compute the measure of association, which one would be appropriate for this test? What do you think it would indicate in terms of strength and direction of the observed relationship?

HINT: Make sure you respond to all of these questions using sentences that make sense!

Answer 1

(1)

Chi square test for independence

because the variables are categorical

(2)

H0: Null Hypothesis: Voting pattern and age are independent.

HA: Research Hypothesis: Voting pattern and age are dependent.

(3)

Degrees of Freedom = (r - 1) X (c - 1)

                               = (2 - 1) X (2 -1) =1

Take = 0.05

From Table, critical value of = 3.8415

(4)

Assuming H0, the Expected Frequencies are obtained as follows:

	Young folks	Older folks	Total
Voted No	11X9/22=4.50	4.50	9
Voted Yes	6.50	6.50	13
Total	11	11	22

Test statistic is calculated as follows:

O	E	(O- E)2/E
5	4.50	0.06
4	4.50	0.06
6	6.50	0.04
7	6.50	0.04
Total = =		0.19

Test statistic = = 0.19

(5) Since calculated value of = 0.19 is less than critical value of = 3,8415, the difference is not significant. Fail to reject null hypothesis.

(6) Conclusion:
From the data, we infer that there is no significant difference in the voting behavior of older and younger folks.