Question

A researcher wants to study the relationship between salary and gender. She randomly selects 330 ... A researcher wants to study the relationship between salary and gender. She randomly selects 330 individuals and determines their salary and gender. Can the researcher conclude that salary and gender are dependent?

Income Male Female Total

Below $25,000 25 16 41

$25,000-$50,000 47 103 150

$50,000-$75,000 48 32 80

Above $75,000 36 23 59

Total 156 174 330

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 men with an income $50,000-$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 0.01 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 0.01 level of significance. Step 8 of 8: State the conclusion of the hypothesis test at the 0.01 level of significance.

Answer 1

Observed	Oi	<25000	25000-50000	50000-75000	>75000	Total
	male	25	47	48	36	156
	female	16	103	32	23	174
	Total	41	150	80	59	330
Expected	Ei=Σrow*Σcolumn/Σtotal	<25000	25000-50000	50000-75000	>75000	Total
	male	19.3818	70.9091	37.8182	27.8909	156
	female	21.6182	79.0909	42.1818	31.1091	174
	Total	41	150	80	59	330
chi square    χ2	=(Oi-Ei)2/Ei	<25000	25000-50000	50000-75000	>75000	Total
	male	1.6285	8.0617	2.7413	2.3577	14.789
	female	1.4601	7.2277	2.4577	2.1138	13.259
	Total	3.089	15.289	5.199	4.471	28.0483

step 1:null hypothesis:salary and gender are independent

alternate hypothesis:Ha salary and gender are not independent

Step 2 of 8: expected value for the number of men with an income below $25,000 =19.4

Step 3 :expected value for the number of men with an income $50,000-$75,000=37.8

Step 4 of 8: value of the test statistic. =28.048

Step 5 of 8:

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

3

  Step 6 of 8:

for 3 df and 0.01 level of signifcance critical region       χ2=

11.345

Step 7 of 8:

reject the null hypothesis

Step 8 of 8:there is sufficient evidence........