1. Astudywantstodetermineifthereturns fromseveralmutual fundsaredifferent.Arandomsample of10observationsforeachfund wascollected.Theworksheet"MutualFund"containsobservations for monthly returns overthe lastyear.

• a) Specify the null and alternative hypothesis for a test to determine if at least one fundperforms differently from the others. Let =.01

H₀: fidelity = Vanguard = S&P 500 Index

H_a: at least one population mean is different

• b) ExplaintheconceptualdifferenceintheANOVAfortheBetweengroup andWithingroup variation.
• c) Report the p-value and perform the test. What is the conclusion of the test? That is, is there enough evidence to suggest that the funds perform differently.Explain youranswer.
• d) Perform a hypothesis test to determine if the Fidelity Group fund performed better than the VanguardRetirementfund.Use=0.05.Stateyournullandalternativehypothesisalongwith the p-value from the test. Explain theresult.

Anova: Single Factor SUMMARY Groups Count Sum Average Variance Fidelity Growth 10 0.862016 0.086202 0.00136 Vanguard Retirement 10 0.625118 0.062512 0.000133 S&P 500 Index Fund 10 0.37556 0.037556 0.000884 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 0.011834671 2 0.005917 7.46829 0.003 5.488118 Within Groups 0.021392858 27 0.000792 Total 0.03322753 29