Question

25 runners and 25 bikers are randomly chosen to do the same race. The runners took 30 minutes to complete the race on average and the standard deviation was 5 minutes. The bikers took 35 minutes to complete the race on average and their standard deviation was 8 minutes. Assume that the race completion times are normally distributed for both groups.

For the following questions, do not use any calculator or MS Excel. All math should be shown using equations and tables.

a) Assuming that standard deviations are known for the populations, show whether (at the 10% significance level) a runner completes the race faster than a biker on average.

- What are the null and alternative hypotheses?

- Calculate the appropriate test statistic.

- Show with the p value or critical value that we reject or fail to reject the null hypothesis.

b) Assuming the standard deviations are UNKNOWN and are sample deviations computed from the above samples. Repeat the questions above from part a with this information.

c) Assume now that we randomly pick 10 athletes and have them perform the race by running and biking, with the order randomly determined, we get a difference sample standard deviation of 8 and difference mean of 3. Repeat question a above with this new information.

Answer 1

Note:Due little confussion about b bit so i couldn't solved if you want to answer for b bit please post it separately

Thank you.