Question

# A researcher wants to study the relationship between salary and gender. She randomly selects 316individuals and...

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?)

 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

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