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9.9. Is gender independent of education level? A random sample of people were surveyed and each person...

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Statistics

9.9. Is gender independent of education level? A random sampleof people were surveyed and

each person was asked to report the highest education level theyobtained. Perform a hypothesis

test. Include all 5 steps.

High SchoolBachelorsMasters
Female306054
Male254044

Answer & Explanation Solved by verified expert
4.1 Ratings (536 Votes)

Null hypothesis: Ho: gender is independent of education level

Alternate hypothesis: HA: gender is dependent of education level

degree of freedom(df) =(rows-1)*(columns-1)= 2
for 2 df and 0.05 level of signifcance critical region       χ2= 5.991
Applying chi square test of independence:
Expected Ei=row total*column total/grand total High school Bachelors Masters Total
female 31.30 56.92 55.78 144
male 23.70 43.08 42.22 109
total 55 100 98 253
chi square    χ2 =(Oi-Ei)2/Ei High school Bachelors Masters Total
female 0.0543 0.1670 0.0567 0.2781
male 0.0718 0.2206 0.0749 0.3673
total 0.1261 0.3876 0.1316 0.6454
test statistic X2 = 0.645

Decision:as test statistic is not in critical region, we fail to reject null hypothesis

Conclusion: we can not conclude that gender is not independent of education level
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