Question

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A researcher wants to study the relationship between salary and gender. She randomly selects 324 individuals and determines their salary and gender. Can the researcher conclude that salary and gender are dependent? Female Total 24 50 38 72 Income Male Below $25,000 26 $25,000-$50,000 34 $50,000-$75,000 42 Above $75,000 53 Total 155 47 89 60 113 169 324 < Prev Copy Data Step 1 of 8: State the null and alternative hypothesis.

Answer 1

Solution Given that Income Male Female Total 50 Below $25,000 24 34 38 72 $25,000 - $50,000 $50,000 $75,000 42 47 89 Above $75,000 53 Go 113 Ho: Salary Total 155 169 324 Step! Now to state the null and alternative hypothesis Null hypothesis Hoi independent and gender are gender are dependent Alternative hypothesis : Salary and So the "option is the corect answer Step 2: number of men with To find the expected value for the an income below Expected Value row total X Column total Grand total Now 50X155 E Below $25,000 and male 7750 324 $ 25,000 4324 23.9 23.9 E Below $25,000 and male

Step-3 To find the expected value for the number of women with an income below $25,000 50X169 E Below $25,000 and female 324 8450 324 = 26.1 E Below $25,000 and female 26.1 Step-4 Now first to find the expected frequencies on each cell Income Male Total Female 50X169 Below $25,000 50x155 324 = 23.920 50 = 26.080 324 $25,000 $50,000 72X155 324 - 34.444 72x 169 - 37.556 324 72 $50,000 - $75,000 89 X 155 89x169 =49.577 324 324 46.423 89 Above $75,000 113X155 324 = 54.059 113X169 324 =58.941 113 155 169 Total 324

3 Now to find the value of the test statistic We know that The formula of x ² statistic is given by x² = (Oi-EP) ? 2 2 Х + 2(26-23.920) (24 - 26.080) (34-34.444)? (38–37.556) + 23.920 26.080 34.444 t 37.556 (42-4.2.571)2 (47-46.423) 2 t (53–54.059) ² + + 42.577 54.059 (60-58.941² + 58.941 46.423 2 X=0.1809+ 0.1659+0.0057 + 0.0052 +0.0078 + 0.0072 +0.02077 0.0190 x² 0.412 Therefore the value of the test statistic is (00412 Step- 5 Now to find the degrees of freedom degrees of freedom (8-1) (C-1). of = (4-1) (2-1) df = (3) (1) af = 3

Step-6 Here &= 0.1 2 =X², df critical Value -Xool, 3 2 = 6.251 2 6.251 critical Value Step-7 : -critical value > x Statistic 6.251 > 0.412 Therefore we fail to reject the null hypothesis (Ho) So the loption-1" is the CU correct answer Step - 8: Conclusion : There is not significant evidence that Salary and gender related. Therefore the option - 2" is the are correct answer.