Directions: Test the following hypotheses using the Traditional Method. You must show all the steps involved and the final statement must be phrased appropriately for the problem.
A sports-shoe manufacturer claims that joggers who wear its brand of shoe will jog faster than those who don't. A sample of eight joggers is taken, and they agree to test the claim on a 1-mile track. The rates (in minutes) of the joggers while wearing the manufacturer's shoe and while wearing any other brand of shoe are shown here. Test the claim at a 2.5% level of significance.
Runner 1 2 3 4 5 6 7 8
Mfg brand 8.2 6.3 9.2 8.6 6.8 8.7 8.0 6.9
Other brand 7.1 6.8 9.8 8.0 5.8 8.0 7.4 8.0
Please see the attached file.
The improvement is calculated as: Time to run 1-mile track while wearing other brand - Time to run 1-mile track while wearing manufacturers' brand. A positive outcome is desired since we want to show that Time to run 1-mile track while wearing manufacturers' brand < Time to ...
This solution looks at a hypothesis test of running shoes with 2.5% significance level.