The TTEST Procedure Variable: distance group Mean Std Dev Std Err Minimum Maximum New formula 10 10.7900 0.8103 0.2562 9.7000 12.1000 Old formula 10 10.6500 0.7106 0.2247 9.7000 11.9000 Diff (1-2) 0.1400 0.7621 0.3408 group Method Mean 95% CL Mean Std Dev 95% CL Std Dev New formula 10.7900 10.2104 11.3696 0.8103 0.5573 1.4793 Old formula 10.6500 10.1416 11.1584 0.7106 0.4888 1.2973 Diff (1-2) Pooled 0.1400 -0.5760 0.8560 0.7621 0.5758 1.1270
To test a newly formulated protein bar designed to improve running performance, a randomized control trial was deisgn recruiting 20 distance runners. Ten participants were randomly assigned to each group (newly formula protein bar vs old bar). Thirty minutes after consuming the bar the participant ran for 2 hours on a treadmill. The distance each participant ran (in km) in each group was recorded.
The data and SAS output is below
|
Runners on New formula |
Runners on Old formula |
|
10.6 |
10.5 |
|
11.2 |
10.9 |
|
10.3 |
10.2 |
|
11.9 |
11.6 |
|
9.8 |
9.7 |
|
11.1 |
10.8 |
|
12.1 |
11.9 |
|
10.9 |
10.8 |
|
9.7 |
9.8 |
|
10.3 |
10.3 |
a) What is the pooled standard deviation, sp?
b) Find a 95% confidence interval for the population mean difference in run distance for those who eat the newly formulated protein bar compared to the old protein bar.
c) Carry out the appropriate hypothesis test using a two-sided alternative - at a 0.01 significance level.
H0: ________________________________
HA: ________________________________
Test Statistic:
Conclusion in context of the study:
d) Briefly discuss why the conclusions between the two study designs differ (question 2 and question 3), even though the data are exactly the same?
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