Suppose we need to determine the average time it takes for an Olympic female freestyle swimmer to complete 100m.We obtain the data from 40 Olympic participants in 2016, and the average time taken for them is 59 seconds with a standard deviation of 3.25 seconds.

a)(2 pts) What is the observational unit in the context?

40 Olympic participants

b)(2 pts) What is the sample and the size of the sample?

c)(2 pts) Write down the observed statistic and assign the appropriate symbol to it.

d)(4 pts) Construct a 95% confidence interval for the true long run average time taken for an Olympic female freestyle swimmer to complete 100m. (Show all your work for full credit)

e)(2 pts) Interpret the above obtained confidence interval.

One of our colleagues think that an Olympic female freestyle swimmer competing in the 100m event is faster than 60 seconds. Considering her claim,

f)(2 pts) In words, state the correct null and alternative hypothesis to test the claim

g)(2 pts) In symbols, state the correct null and alternative hypothesis to test the claim

h)(2 pts) Based on the confidence interval that you calculated in part e), would you reject or fail to reject the null hypothesis? Why or why not?

i)(2 pts) What is your conclusion based on part h?