Context: A clinical study is comparing the effectiveness of three different exercise regimens (light, moderate, intense) on the weight loss of patients over a 6-month period. You are provided with the data showing the weight loss (in kilograms) for 30 patients, 10 from each exercise group.

Task:

• Perform a One-Way ANOVA in SAS to determine whether there is a statistically significant difference in the mean weight loss across the three exercise groups.
• State the null and alternative hypotheses:
  • Null Hypothesis (H): The mean weight loss is the same across all three exercise regimens.
  • Alternative Hypothesis (H): At least one group has a different mean weight loss.
• Use a significance level of = 0.05.
• In SAS, use the PROC ANOVA or PROC GLM procedure to calculate the F-statistic and p-value.
• Based on the results, state whether you reject or fail to reject the null hypothesis.
• If significant differences are found, perform a post-hoc test (e.g., Tukey's HSD) in SAS to determine which specific exercise groups differ.
• Provide an interpretation of the results in the context of the study.

Data (Weight loss for 30 patients across three exercise regimens): (Use the following dataset for the analysis, and students will input this into SAS)

• Light Exercise: 2.1, 3.0, 2.8, 3.3, 3.1, 2.5, 2.9, 3.2, 2.7, 3.0
• Moderate Exercise: 4.2, 4.0, 4.5, 4.1, 4.6, 4.2, 4.3, 4.4, 4.2, 4.1
• Intense Exercise: 5.8, 6.0, 6.1, 5.7, 6.3, 6.2, 5.9, 6.1, 5.8, 6.0

Part II: Two-Way ANOVA Using SAS

Context: In a pharmaceutical trial, researchers are studying the combined effect of treatment type (Drug A, Drug B) and dosage level (low, medium, high) on cholesterol reduction in patients with high cholesterol. You are provided with cholesterol reduction data for 5 patients in each group, for a total of 30 patients.

Task:

• Perform a Two-Way ANOVA in SAS to analyze the effect of treatment type and dosage level on cholesterol reduction, as well as the interaction between these two factors.
• State the hypotheses:
  • Null Hypothesis (H): There is no difference in cholesterol reduction between treatment types and dosage levels, and there is no interaction effect.
  • Alternative Hypothesis (H): There is a difference in cholesterol reduction due to treatment type, dosage level, or their interaction.
• Use PROC GLM in SAS to run the Two-Way ANOVA.
• Test for the main effects of treatment type and dosage level, as well as the interaction effect.
• Interpret the p-values for each main effect and the interaction. Discuss whether treatment type, dosage level, or their interaction significantly affects cholesterol reduction.
• Provide a conclusion based on the results.

Data (Cholesterol reduction for 30 patients, grouped by treatment type and dosage level): (Use the following dataset for the analysis, and students will input this into SAS)

Treatment	Dosage	Cholesterol Reduction (mg/dL)
Drug A	Low	15, 14, 16, 17, 16
Drug A	Medium	20, 19, 21, 22, 21
Drug A	High	25, 24, 26, 27, 26
Drug B	Low	13, 14, 15, 14, 13
Drug B	Medium	18, 19, 17, 18, 19
Drug B	High	23, 22, 24, 23, 22

Submit: Your SAS output showing the ANOVA tables, test statistics, and post-hoc test results. Also submit a written report explaining the results of both the One-Way and Two-Way ANOVA tests, including:

• • The interpretation of the F-statistic and p-values.
• • Conclusions on whether there are significant differences between groups and any interaction effects.
  • Recommendations or insights based on the analysis.