Asked by Salah Suwaileh on May 11, 2024
Verified
The following data shows annual income,in thousands of dollars,categorized according to the two factors of gender and level of education.Assume that incomes are not affected by an interaction between gender and level of education,and test the null hypothesis that gender has no effect on income and that level of education has no effect on income.Use a 0.05 significance level. Female Male High school 23,27,24,2625,26,22,24 University 28,36,31,3335,32,39,28 Advanced degree 41,38,43,4935,50,47,44\begin{array} { l c c } & \text { Female } & \text { Male } \\\text { High school } & 23,27,24,26 & 25,26,22,24 \\\text { University } & 28,36,31,33 & 35,32,39,28 \\\text { Advanced degree } & 41,38,43,49 & 35,50,47,44\end{array} High school University Advanced degree Female 23,27,24,2628,36,31,3341,38,43,49 Male 25,26,22,2435,32,39,2835,50,47,44
Annual Income
The total amount of income earned over a year from work, business, investments, or other sources.
Level of Education
Refers to the ultimate stage of formal learning or highest degree obtained by an individual.
- Investigate ANOVA (Analysis of Variance) tables for hypothesis testing concerning differences in group means.
- Examine the findings of ANOVA assessments, specifically the F-ratio and p-value, for statistical decision-making.
- Generate hypotheses for both null and alternative scenarios pertaining to ANOVA.
Verified Answer
D-
Dylan - - -May 16, 2024
Final Answer :
H0: γ1 = γ2,where γ represents gender.HA: gender has an effect on income.The test statistic is F=0.16954F = 0.16954F=0.16954 ,and the corresponding P-value \text { P-value } P-value is 0.6849.Because the P-value \text { P-value } P-value is greater than 0.05,we fail to reject the null hypothesis that gender has no effect on income. H0\mathrm { H } _ { 0 }H0 : τ1 = τ2 = τ3,where τ represents level of education.HA: Education level has an effect on income.The test statistic is F = 44.96689,and the corresponding P-value \text { P-value } P-value is 0.0000000397.Because the P-value \text { P-value } P-value is less than 0.05,we reject the null hypothesis that education level has no effect on income.It appears that education level does have an effect on income.
Learning Objectives
- Investigate ANOVA (Analysis of Variance) tables for hypothesis testing concerning differences in group means.
- Examine the findings of ANOVA assessments, specifically the F-ratio and p-value, for statistical decision-making.
- Generate hypotheses for both null and alternative scenarios pertaining to ANOVA.
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