7 statistics

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) 97, 607 ANOVA Results Connecticut (CT) 96,224 F P-value Massachusetts (MA) 85,790 2.37 0.0653 Vermont (VT) 77,903 Maine (ME) 77,471 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? O HO: UNH = MCT = MMA = HVT = HME. OHO : HNH * MCT # HMA # MVT # HME. Ho: At least one of the population means is different from the others. OHO : HNH > HCT > HMA > HVT > HME . (b) What is the alternate hypothesis for this test? O H1: HNH = HCT = HMA = HVT = HME. OH 1 : UNH * MCT # HMA # HVT # HME. OH 1 : HNH > HCT > HMA > HVT > HME. H1: At least one of the population means is different from the others. (c) What is the conclusion regarding the null hypothesis at the 0.05 significance level? reject Ho fail to reject Ho (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 0.10 significance level? Yes No