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

Comprehensive study on hypothesis testing using chi-square and nonparametric methods.

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    Statistical Analysis of Chi - Square Tests and Nonparametric Tests: A Comprehensive Study on Hypothesis Testing and Interpretation 1. Using StatCrunch, calculate the chi - square statistic and degre es of freedom for the following set of data for 300 people: Group A Group B Group C Total Had flu shot 20 30 32 82 Didn’t have flu shot 80 70 68 218 Total 100 100 100 300 Is the value of the chi - square statistically significant at the 0.05 level? The output of Chi - Square test for independence obtained through StatCrunch is shown below. Contingency table results: Rows: Had Flu shot Columns: Group Chi - Square test for independence: Cell format Count Expected count Contributions to Chi - Square Group A Group B Group C Total Had Flu shot Count Expected count Contributions to Chi - Square 20 (27.33) (1.967) 30 (27.33) (0.2602) 32 (27.33) (0.7967) 82 Didn't have Flu shot Count Expected count Contributions to Chi - Square 80 (72.67) (0.7401) 70 (72.67) (0.0979) 6 8 (72.67) (0.2997) 218 Total 100 100 100 300 Measure DF Value P - value

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    Since P - value of the test = 0.1248 > α = 0.05, the value of the chi - square is not statistically significant 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 “ Had Flu shot” and “Group”. The research hypothesis of interest is to test whether, H a : The attributes “ Had Flu shot” and “Group” are not independent. against the null hypothesis, H 0 : The attributes “ Had Flu shot” and “Group” are independent. ( Claim ) The test statistic χ 2 (2) = 4.162, p = 0.1248 > α = 0.05, indicates that the value of the chi - square is not statistically significant at the 0.05 level . Therefore, at 0.05 level reported results provide no sufficient evidence to reject the claim that the attributes “ Had Flu shot” 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 following set of data for 180 people undergoing a knee replacement treatment with a drug supplement: Treatment with drug X Treatment without Drug X Total Had > 8 wk rehab 18 32 50 Had < 8 wk rehab 70 60 130 Total 88 92 180 Is the value of the chi - square statistically significant at the 0.05 level? The output of Chi - Square test for independence obtained through StatCrunch is shown below. Contingency table results: Rows: Had > 8wk rehab Columns: Treatment with drug X Chi - Square 2 4.162005 0.1248

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