Question

A researcher wants to study the relationship between salary and gender. She randomly selects 324324 individuals and determines their salary and gender. Can the researcher conclude that salary and gender are dependent?

Below $25,000$⁢25,000	26	17	43
$25,000$⁢25,000-$50,000$⁢50,000	37	26	63
$50,000$⁢50,000-$75,000$⁢75,000	36	90	126
Above $75,000$⁢75,000	56	36	92
Total	155	169	324

Find the value of the test statistic. Round your answer to three decimal places.

part 5 find the degrees of freedom associated with the test statistic for this problem.

part 6 Find the critical value of the test at the 0.010.01 level of significance. Round your answer to three decimal places.

part 7

Make the decision to reject or fail to reject the null hypothesis at the 0.010.01 level of significance.

part 8

Make the decision to reject or fail to reject the null hypothesis at the 0.010.01 level of significance.

Answer 1

Observed	Gender	Total
	Male	Female
Below $25,000$⁢25,000	26	17	43
$25,000$⁢25,000-$50,000$⁢50,000	37	26	63
$50,000$⁢50,000-$75,000$⁢75,000	36	90	126
Above $75,000$⁢75,000	56	36	92
Total	155	169	324

Expected value of a cell= Row total * col total / overall total

Expected	Gender	Total
	Male	Female
Below $25,000$⁢25,000	20.5710	22.4290	43
$25,000$⁢25,000-$50,000$⁢50,000	30.1389	32.8611	63
$50,000$⁢50,000-$75,000$⁢75,000	60.2778	65.7222	126
Above $75,000$⁢75,000	44.0123	47.9877	92
Total	155	169	324

	Gender
	Male	Female
Below $25,000$⁢25,000	1.4328	1.3141
$25,000$⁢25,000-$50,000$⁢50,000	1.5619	1.4325
$50,000$⁢50,000-$75,000$⁢75,000	9.7782	8.9682
Above $75,000$⁢75,000	3.2651	2.9946

There is no relationship between gender and salary.

There is a relationship between gender and salary.

Chi -square test STat =

Test Stat = 30.7475

df = (r -1) * (c -1) ...................... r = no. of rows and c = no. of columns

= 3 * 1

df = 3

level of significance = 0.01

C.V. =

=                     .................using chi-square tables

Critical value = 11.345 ..................we use chi-square probabiltiy ditribution tables for it.

Since Test Stat > C.V.

We reject the null hypothesis at 1% level of significance. There is sufficient evidence to conclude that there is a relationship between gender and salary.

level of significance = 0.1

C.V. =

=                     .................using chi-square tables

Critical value = 6.2514 ..................we use chi-square probabiltiy ditribution tables for it.

Since Test Stat > C.V.

We reject the null hypothesis at 10% level of significance. There is sufficient evidence to conclude that there is a relationship between gender and salary.