Question

A study was undertaken to investigate the effectiveness of an aquarobic exercise program for patients with osteoarthritis. A convenience sample of 70 individuals with arthritis was selected, and each person was randomly assigned to one of two groups. The first group participated in a weekly aquarobic exercise program for 8 weeks; the second group served as a control. Several pieces of data were collected from the individuals, including their total cholesterol (mg).

Determine if there is a significant difference in the mean cholesterol for the two groups (aquarobic & control) at the start of the study using a significance level of 0.10.   

Difference	Sample Diff.	Std. Error	df
Aquarobic - Control	-0.9992	7.8858	59.1441

• What hypotheses should be tested? Make sure to select the hypotheses which are written with notation consistent with the type of samples selected.

  Ho:μ1=μ2Ho:μ1=μ2
  Ha:μ1>μ2Ha:μ1>μ2

  Ho:μ1=μ2Ho:μ1=μ2
  Ha:μ1≠μ2Ha:μ1≠μ2

  Ho:μd=0Ho:μd=0
  Ha:μd≠0Ha:μd≠0

  Ho:μ1=μ2Ho:μ1=μ2
  Ha:μ1<μ2Ha:μ1<μ2

  Ho:μd=0Ho:μd=0
  Ha:μd<0Ha:μd<0

  Ho:μd=0Ho:μd=0
  Ha:μd>0Ha:μd>0

• αα  =
• TS: t =   (round to 3 decimal places)
• probability = Select an answer 0.4497 0.8994 0.5503
• decision: Select an answer reject H₀ fail to reject H₀
• What conclusion is reached based upon the decision made in your test?
  • At the 0.10 level, there is not sufficient evidence to conclude there is a difference in the mean cholesterol of individuals participating in the aquarobic program and those in the control group.
  • At the 0.10 level, there is sufficient evidence to conclude there is a difference in the mean cholesterol of individuals participating in the aquarobic program and those in the control group.

After the 8-week program, those who participated in the aquarobic program had their ending cholesterol measured, and the change in cholesterol was recorded for each participant. Estimate the mean cholesterol change using 90% confidence.

• The formula which should be used for this interval is:
  • (¯y1−¯y2)±t√s21n1+s22n2(y¯1-y¯2)±ts12n1+s22n2
  • ¯yd±tsd√ndy¯d±tsdnd
• With % confidence, we estimate that the mean cholesterol before participating in 8 weeks of aquarobics is between mg and mg  than the mean cholesterol after participation. Note: Round the limits of your interval to three decimal places. In the last box type the appropriate word - more or less. Think carefully about what positive and negative differences mean about the change in cholesterol based on how the differences were taken.

Difference	Sample Diff.	Std. Error	Critical Pt
Pre - Post	18.4433	1.1245	1.6909

A 90% confidence interval was also calculated for the change in total cholesterol (pre - post) for the control group. That interval was found to be (-2.005, 2.192). Based on this interval and the one which you calculated for the aquarobic group, what conclusion would you draw?

• Neither group had a significant change in mean cholesterol.
• The control group did not have a significant change in mean cholesterol, while the aquarobic group had a significant decrease in mean cholesterol.
• The mean cholesterol for the control group increased, while the aquarobic group had a significant decrease in mean cholesterol.
• Both groups had a significant decrease in mean cholesterol. However, the decrease for the aquarobic group was larger.
• The aquarobic group did not have a significant change in mean cholesterol, while the control group had a significant increase in mean cholesterol.

Answer 1

Prob. 1:

decision: fail to reject H0

At the 0.10 level, there is not sufficient evidence to conclude there is a difference in the mean cholesterol of individuals participating in the aquarobic program and those in the control group.

With 90% confidence, we estimate that the mean cholesterol before participating in 8 weeks of aquarobics is between 14.177mg less and 12.179mg more than the mean cholesterol after participation.

Problem 2:

90% confidence interval for the change in total cholesterol (pre - post) for the aquarobic group:

(18.4433-1.6909*1.1245, =(16.5419, 20.3447).

Since the CI contains only positive values so the aquarobic group had a significant decrease in mean cholesterol.

Howerver  CI for control group contains zero so the control group did not have a significant change in mean cholesterol.

Hence Option: The control group did not have a significant change in mean cholesterol, while the aquarobic group had a significant decrease in mean cholesterol.