Question

To test a newly formulated protein bar designed to improve running performance, 10 distance runners performed two trials.  All the participants ate the new protein formula bar on the first trial. In the second trial, the same participants ate the regular (old) protein bar. Thirty minutes after consuming the bar the participant ran for 2 hours on a treadmill.

At the end of the two trials, performed on consecutive days for each participant, the distance each participant ran (in km) was recorded. The data is below.

Runner	New formula	Old formula
1	10.6	10.5
2	11.2	10.9
3	10.3	10.2
4	11.9	11.6
5	9.8	9.7
6	11.1	10.8
7	12.1	11.9
8	10.9	10.8
9	9.7	9.8
10	10.3	10.3

a. Comment on the validity of the study design and any ways you can think of to improve the design?

b. Calculate a 99% confidence interval for the population mean difference in run distance after eating 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: ________________________________

H₁: ________________________________

Name of test:   __________________________

Test Statistic:

Define the rejection region:

Calculate the p-value:

Conclusion in context of the study:

Answer 1