Question

Income by State: A student at a private college in New England wants to see if there is a difference in mean household incomes for students from the various New England states. The tables below give the sample sizes and means from her study and the results of an ANOVA test run on this data. She wants to test for a difference in mean household income for all students between the five states.

Student's	Sample	Mean Household
State	Size	Income (x)
New Hampshire (NH)	9	97,607
Connecticut (CT)	12	96,224
Massachusetts (MA)	17	85,790
Vermont (VT)	11	77,903
Maine (ME)	5	77,471

  

ANOVA Results

F	P-value
2.37	0.0653

The Test: Complete the steps in testing for a difference in mean household income for all students between the five states.

(a) What is the null hypothesis for this test?

H₀: At least one of the population means is different from the others. H₀: μ_NH ≠ μ_CT ≠ μ_MA ≠ μ_VT ≠ μ_ME.     H₀: μ_NH = μ_CT = μ_MA = μ_VT = μ_ME. H₀: μ_NH > μ_CT > μ_MA > μ_VT > μ_ME.

(b) What is the alternate hypothesis for this test?

H₁: At least one of the population means is different from the others. H₁: μ_NH ≠ μ_CT ≠ μ_MA ≠ μ_VT ≠ μ_ME.     H₁: μ_NH > μ_CT > μ_MA > μ_VT > μ_ME. H₁: μ_NH = μ_CT = μ_MA = μ_VT = μ_ME.

(c) What is the conclusion regarding the null hypothesis at the 0.10 significance level?

reject H₀ fail to reject H₀    

(d) Choose the appropriate concluding statement.

We have proven that the mean household incomes for all students from the different states are equal. There is sufficient evidence to conclude that the mean household incomes for all students from the different states are different.     There is not enough evidence to conclude that the mean household incomes for all students from the different states are different.

(e) Does your conclusion change at the 0.05 significance level?

Yes No    

Answer 1

Answer

ANOVA Results

F	P-value
2.37	0.0653

(A) option C is correct because we assume that the claim is incorrect and all the means are equal.

H₀: μ_NH = μ_CT = μ_MA = μ_VT = μ_ME

(B) Alternate hypothesis is the testing statement,i.e. there is a difference in mean household incomes for students from the various New England states

so, option A is correct

H₁: At least one of the population means is different from the others.

(C) Reject Ho as we can see that the result is significant at 0.10 significance level because the p value is less than significance level 0.10

(D) We have rejected the null hypothesis, so we must have evidence to support the alternate hypothesis

There is sufficient evidence to conclude that the mean household incomes for all students from the different states are different

(E) Yes, because the p value is greater than significance level, i.e. 0.0653 > 0.05