Question

A researcher wants to study the relationship between salary and gender. She randomly selects 384 individuals and determines their salary and gender. Can the researcher conclude that salary and gender are dependent?

Step 1 of 8: State the null and alternative hypothesis.

Step 2 of 8: Find the expected value for the number of men with an income below $25,000. Round your answer to one decimal place.

Step 3 of 8:

Find the expected value for the number of women with an income above $75,000. Round your answer to one decimal place.

Step 4 of 8:

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

Step 5 of 8: Find the degrees of freedom associated with the test statistic for this problem.

Step 6 of 8:

Find the critical value of the test at the 0.05 level of significance. Round your answer to three decimal places.

Step 7 of 8:

Make the decision to reject or fail to reject the null hypothesis at the 0.05 level of significance.

Step 8 of 8: State the conclusion of the hypothesis test at the 0.05 level of significance.

Income	Male	Female	Total
Below $25,000	31	84	115
$⁢25,000-$50,000	59	45	104
$⁢50,000-$75,000	30	20	50
Above $75,000	65	50	115
Total	185	199	384

Answer 1

step 1:

Null hypothesis: salary and gender are independent

Alternate hypothesis: salary and gender are dependent

Step 2 of 8: expected value =row total*column total/grand total =185*115/384 =55.4

Step 3 of 8:expected value =199*115/384 =59.6

Step 4 of 8:

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	male	female	Total
	<25000	55.404	59.596	115
	25000-50000	50.104	53.896	104
	5000-75000	24.089	25.911	50
	>75000	55.404	59.596	115
	total	185	199	384
chi square    χ2	=(Oi-Ei)2/Ei	male	female	Total
	<25000	10.749	9.993	20.7419
	25000-50000	1.579	1.468	3.0477
	5000-75000	1.451	1.349	2.7993
	>75000	1.662	1.545	3.2074
	total	15.4414	14.3550	29.7964
test statistic X2=		29.796

Step 5 of 8:

degree of freedom(df) =(rows-1)*(columns-1)=

3

Step 6 of 8:

for 3 df and 0.05 level,critical value χ2=

7.815

Step 7 of 8:

reject the null

Step 8 of 8:

we have sufficient evidence to conclude that salary and gender are dependent