An adventure company runs two obstacle courses, Fundash and Coolsprint. The designer of the courses suspects that the mean completion time of Fundash is not equal to the mean completion time of Coolsprint. To test this, she selects290.Fundash runners and220Coolsprint runners. (Consider these as random samples of the Fundash and Coolspring runners.) The290 Fundash runners complete the course with a mean time of63.6 minutes and a standard deviation of2.9 minutes. The220 Coolsprint runners complete the course with a mean time of63.0

minutes and a standard deviation of2.7 minutes. Assume that the population standard deviations of the completion times can be estimated to be the sample standard deviations, since the samples that are used to compute them are quite large. At the0.01level of significance, is there enough evidence to support the claim that the mean completion time,1, of Fundash is not equal to the mean completion time,2, of Coolsprint? Perform a two-tailed test. Then complete the parts below.

Carry your intermediate computations to at least three decimal places. (If necessary, consult alist of formulas.)

(a)State the null hypothesisH

0

and the alternative hypothesisH

1

.H

0

:

H

1

:

(b)Determine the type of test statistic to use.

(Choose one)

(c)Find the value of the test statistic. (Round to three or more decimal places.)

(d)Find thep-value. (Round to three or more decimal places.)

(e)Can we support the claim that the mean completion time of Fundash is not equal to the mean completion time of Coolsprint?YesNo