Question

A researcher wants to study the relationship between salary and gender. She randomly selects 316individuals and determines their salary and gender. Can the researcher conclude that salary and gender are dependent?

Income	Male	Female	Total
Below $25,000$	36	68	104
$⁢25,000-$50,000	54	43	97
$⁢50,000-$75,000	42	31	73
Above $75,000	23	19	42
Total	155	161	316

-Find the critical value of the test at the 0.01 level of significance. Round your answer to three decimal places.

-Make the decision to reject or fail to reject the null hypothesis at the 0.01 level of significance?

-State the conclusion of the hypothesis test at the 0.01 level of significance? (Sufficient evidence or not sufficient evidence?)

Answer 1

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	male	female	Total
	<25000	51.01	52.99	104
	25000-50000	47.58	49.42	97
	50000-75000	35.81	37.19	73
	>75000	20.60	21.40	42
	total	155	161	316
chi square    χ2	=(Oi-Ei)2/Ei	male	female	Total
	<25000	4.4181	4.2535	8.6716
	25000-50000	0.8665	0.8342	1.7007
	50000-75000	1.0711	1.0312	2.1023
	>75000	0.2793	0.2689	0.5482
	total	6.6351	6.3878	13.0228
test statistic X2 =		13.023

for 3 df and 0.01 level , critical value       χ2=

11.345

reject the null hypothesis at the 0.01 level of significance

Sufficient evidence