Marathon runners: carry water for the marathon? yes or no

long races, like a marathon, have hydration stations about 2-3 miles apart. when it comes to getting ready for the big race, runners must decide whether the hydration stations is enough to get them through the race or whether they should carry their own supply of water. some runners believe carrying additional weight (like a water bottle) will slow them down and therefore they decide to rely on the hydration stations along the race. to put this theory to the test, a random sample of 466 marathon runners is selected and various variables are recorded including the runner’s completion time in minutes (variable: runtime) and whether or not the runner carried water during the race (variable: waterload), the data set calledmarathon. rdata contains the information from the 466 marathon runners selected at random.

a. we would like to assess if, on average, carrying a water bottle during the race slows down the marathon runner. a 5% significance level will be used. define the parameter µ1 as the population mean marathon completion time in minutes when the runner is not carrying their own water bottle and µ2 as the population mean marathon completion time in minutes when the runner is carrying their own water bottle. the null hypothesis can be stated as h0: µ1 = µ2. which of the following is the appropriate direction for the alternative hypothesis ha: µ1 µ2?
greater than (> )
less than (< )
not equal to (≠)

b. use r to perform the two-sample t-test. generate both the pooled and unpooled (general) two independent samples test results. copy and paste both sets of test results below or save the test output as a jpg and upload it.

c. to you decide which of the two test results to use, you suggest that levene's test be conducted. which of the following is the appropriate null hypothesis for levene’s test stated in words?

1. the two sample variances are equal.
2. the two sample variances are similar.
3.the two population variances are equal.
4.the two population variances are similar.