Question

A clinical trial is run to assess the effects of different forms of regular exercise on HDL levels in persons between the ages of 18 and 29. Participants in the study are randomly assigned to one of three exercise groups - Weight training, Aerobic exercise or Stretching/Yoga – and instructed to follow the program for 8 weeks. Their HDL levels are measured after 8 weeks and are summarized below.

The research question is to test if there is a significant difference in mean HDL levels among the exercise groups? Run the test at a 5% level of significance. Which test statistics should be used?

Below is the ANOVA table generated by statistical software. Based on the information, what is the critical value?

Below is the ANOVA table generated by statistical software. Based on the information, do we reject H0 and why (explain your answer below)?

4. A clinical trial is run to assess the effects of different forms of regular exercise on HDL levels in persons between the ages of 18 and 29. Participants in the study are randomly assigned to one of three exercise groups - Weight training, Aerobic exercise or Stretching/Yoga - and instructed to follow the program for 8 weeks. Their HDL levels are measured after 8 weeks and are summarized below. (12 points, 4 points each) Exercise Group N Mean Std Dev Weight Training 20 49.7 10.2 Aerobic Exercise 20 43.111.1 Stretching Yoga 20 57.0 12.5 a) The research question is to test if there is a significant difference in mean HDL levels among the exercise groups? Run the test at a 5% level of significance. Which test statistics should be used? b) The research question is to test if there is a significant difference in mean HDL levels among the exercise groups? Run the test at a 5% level of significance. Below is the ANOVA table generated by statistical software. Based on the information, what is the critical value? Source Sums of Squares Df Mean Squares F 7.56 Between Within Total 1933.73 7286.50 9220.23 2 57 59 966.87 127.83 c) Below is the ANOVA table generated by statistical software. Based on the information, do we reject H, and why (explain your answer below)? Source Sums of Squares Dr Mean Squares F Between 1933.73 2 966.87 7.56 Within 7286.50 57 127.83 Total 9220.23 59

Answer 1

(a) The F-statistic should be used here.

(b) The critical value is 3.159.

(c) Since 7.56 > 3.159, we can reject the null hypothesis.