# Respons e feedbac k none given out of 34 points a

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Respons e Feedbac k: [None Given] Question 36 3.4 out of 3.4 points A study is designed to investigate whether there is a difference in response to various treatments in patients with Rheumatoid arthritis. The outcome is the patient’s self-reported effect of treatment. The data are shown below. Is there a significant difference in effect of treatment? Run the test at a 5% level of significance. Symptoms Worsened No Effect Symptoms Improved Total Treatment 1 22 14 14 50 Treatment 2 14 15 21 50 Treatment 3 9 12 29 50 Selecte d Answer: Null hypothesis: There is no significant difference in the effect of treatment Alternate hypothesis: There is a significant difference in the effect of treatment Chi-Square Test Observed Frequencies Column variable Calculations
Row variable C1 C2 C3 Total fo-fe T1 22 14 14 50 7.0000 T2 14 15 21 50 -1.0000 T3 9 12 29 50 -6.0000 Total 45 41 64 150 Expected Frequencies Column variable Row variable C1 C2 C3 Total (fo-fe)^2/fe T1 15.0000 13.6667 21.3333 50 3.2667 T2 15.0000 13.6667 21.3333 50 0.0667 T3 15.0000 13.6667 21.3333 50 2.4000 Total 45 41 64 150 Data Level of Significance 0.05 Number of Rows 3 Number of Columns 3 Degrees of Freedom 4
Results Critical Value 9.488 Chi-Square Test Statistic 11.356 0 p -Value 0.0228 Reject the null hypothesis Calculated chi-square =11.356 Chi-square value at 0.05 level =9.488 Calculated chi-square =11.356 > 9.488 the table value. The null hypothesis is rejected. There is a significant difference in the effect of treatment. Yes Respons e Feedbac k: [None Given] Question 37 3.4 out of 3.4 points Using the data below, suppose we focus on the proportions of patients who show improvement. Is there a statistically significant difference in the proportions of patients who show improvement between treatments 1 and 2. Run the test at a 5% level of significance. Symptoms Worsened No Effect Symptoms Improved Total Treatment 1 22 14 14 50 Treatment 2 14 15 21 50 Treatment 3 9 12 29 50
= 0.05 (a) The Hypothesis: H0: p 1 = p 2 : The proportion of patients who show improvement after treatment 1 is equal to the proportion of patients who show improvement after treatment 2. Ha: p 1 p 2 : The proportion of patients who show improvement after treatment 1 is different from the proportion of patients who show improvement after treatment 2 This is a 2 Tailed Test. The Test Statistic: The p Value: The p value (2 Tail) for Z = -1.47, is; p value = 0.1416 The Critical Value: The critical value (2 tail) at = , Zcritical = +1.96 and -1.96 The Decision Rule: If Zobserved is > Zcritical or Zobserved is < -Zcritical, Then Reject H0. Also, If the P-value is <, Then Reject H0. The Decision: Since Z lies in between +1.96 and -1.96, We Fail To Reject H0 Also since P value (0.1416) is > (0.05), We Fail to Reject H0. The Conclusion: There isn't-insufficient evidence at the 95% significance level to conclude that the proportion of patients who show improvement after treatment 1 is significantly different from the proportion of patients who show improvement after treatment 2.