A study was undertaken to investigate the effectiveness of anaquarobic exercise program for patients with osteoarthritis. Aconvenience sample of 70 individuals with arthritis was selected,and each person was randomly assigned to one of two groups. Thefirst group participated in a weekly aquarobic exercise program for8 weeks; the second group served as a control. Several pieces ofdata were collected from the individuals, including their totalcholesterol (mg).
Determine if there is a significant difference in the meancholesterol for the two groups (aquarobic & control) at thestart of the study using a significance level of 0.10. Â
| Difference | Sample Diff. | Std. Error | df |
| Aquarobic - Control | -0.9992 | 7.8858 | 59.1441 |
- What hypotheses should be tested? Make sure to select thehypotheses which are written with notation consistent with the typeof 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 =Â Â Â (round to 3 decimal places)
- probability = Select an answer 0.4497 0.8994 0.5503
- decision: Select an answer reject Hâ‚€ fail to reject Hâ‚€
- What conclusion is reached based upon the decision made in yourtest?
- At the 0.10 level, there is not sufficient evidence to concludethere is a difference in the mean cholesterol of individualsparticipating in the aquarobic program and those in the controlgroup.
- At the 0.10 level, there is sufficient evidence to concludethere is a difference in the mean cholesterol of individualsparticipating in the aquarobic program and those in the controlgroup.
After the 8-week program, those who participated in theaquarobic program had their ending cholesterol measured, and thechange in cholesterol was recorded for each participant. Estimatethe 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 beforeparticipating in 8 weeks of aquarobics is between mg andmg  than the mean cholesterol after participation.Note: Round the limits of your interval to threedecimal places. In the last box type the appropriate word -more or less. Think carefully about what positiveand negative differences mean about the change in cholesterol basedon 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 intotal cholesterol (pre - post) for the control group. That intervalwas found to be (-2.005, 2.192). Based on this interval and the onewhich you calculated for the aquarobic group, what conclusion wouldyou draw?
- Neither group had a significant change in meancholesterol.
- The control group did not have a significant change in meancholesterol, while the aquarobic group had a significant decreasein mean cholesterol.
- The mean cholesterol for the control group increased, while theaquarobic group had a significant decrease in meancholesterol.
- 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 meancholesterol, while the control group had a significant increase inmean cholesterol.
