Statistical Analysis of Chi-Square Tests and Nonparametric Tests: A Comprehensive Study on Hypothesis Testing and Interpretation

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Statistical Analysis of Chi-Square Tests and Nonparametric Tests: AComprehensive Study on Hypothesis Testing and Interpretation1.Using StatCrunch, calculate the chi-square statistic and degrees of freedom for the followingset of data for 300 people:Group AGroup BGroup CTotalHad flu shot20303282Didn’t have flu shot807068218Total100100100300Is the value of the chi-square statistically significant at the 0.05 level?The output ofChi-Square test for independenceobtained through StatCrunch is shown below.Contingency table results:Rows:HadFlu shotColumns: GroupChi-Square test for independence:Cell formatCountExpected countContributions to Chi-SquareGroup AGroup BGroup CTotalHad Flu shotCountExpected countContributions to Chi-Square20(27.33)(1.967)30(27.33)(0.2602)32(27.33)(0.7967)82Didn't have FlushotCountExpected countContributions to Chi-Square80(72.67)(0.7401)70(72.67)(0.0979)68(72.67)(0.2997)218Total100100100300MeasureDFValueP-value

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Since P-value of the test = 0.1248 >α= 0.05,the value of the chi-squareis notstatisticallysignificant at the 0.05 level.2.Write a paragraph summarizing the results of the analysis in Exercise 1.The study in Exercise 1 is about the independence of the attributes “HadFlu shot” and “Group”.The research hypothesis of interest is to test whether,Ha: The attributes “HadFlu shot” and “Group” are not independent.against the null hypothesis,H0: The attributes “HadFlu shot” and “Group” are independent.(Claim)The test statisticχ2(2) = 4.162, p = 0.1248 >α= 0.05, indicates thatthe value of the chi-squareis notstatistically significant at the 0.05 level.Therefore, at 0.05 level reported results provide no sufficient evidence torejectthe claim that theattributes “HadFlushot” and “Group” are independent.That means there is no effective of the“Group” on “Having Flu Shot”.3.Using StatCrunch, calculate the chi-square statistic and degrees of freedom for the followingset of data for 180 people undergoing a knee replacement treatment with a drug supplement:Treatment with drug XTreatment without Drug XTotalHad > 8 wk rehab183250Had < 8 wk rehab7060130Total8892180Is the value of the chi-square statistically significant at the 0.05 level?The output ofChi-Square test for independenceobtained through StatCrunch is shown below.Contingency table results:Rows:Had>8wk rehabColumns: Treatmentwith drugXChi-Square24.1620050.1248

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