Question

A sample of 150 individuals (males and females) was surveyed, and the individuals were asked to indicate their yearly incomes. Their incomes were categorized as follows.

Category 1	$20,000	up to	$40,000
Category 2	$40,000	up to	$60,000
Category 3	$60,000	up to	$80,000

Income Category	Male	Female
Category 1	10	30
Category 2	35	15
Category 3	15	45

We want to determine if yearly income is independent of gender.

a. Compute the test statistic.

b. Using the p-value approach, test to determine if yearly income is independent of gender. Use α = .05. Briefly discuss.

Answer 1

(a)

H0: Null Hypothesis: Yearly income is independent of gender

HA: Alternative Hypothesis: Yearly income is dependent on gendr.

Observed Frquencies:

	Male	Female	Total
Category 1	10	30	40
Category 2	35	15	50
Categoty 3	15	45	60
Total	60	90	150

Assuming H0, The Expected Frequencies are calculated as follows:

Expected Frquencies:

	Male	Female	Total
Category 1	60X40150=16	24	40
Category 2	20	30	50
Categoty 3	24	36	60
Total	60	90	150

From the aboveTables, Table is formed as follows:

O	E	(O - E)2/E
10	16	2.25
30	24	1.50
35	20	11.25
15	30	7.50
15	24	3.38
45	36	2.25
Total==		28.125

So

Test statistic is:

28.125

(b)

ndf = (r - 1) X (c - 1) = (3 - 1) X (2- 1) = 2

By Technology, p-value is less than 0.00001. Since p-value is less than , the difference is significant. Reject null hypothesis. The do not support the claim that yearly icome is independent of gender.