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 selects 265 Fundash runners and 290 Coolsprint runners. (Consider these as random samples of the Fundash and Coolspring runners.) The 265 Fundash runners complete the course with a mean time of 63.6 minutes and a standard deviation of 2.9 minutes. The 290 Coolsprint runners complete the course with a mean time of 63.0 minutes and a standard deviation of 2.6 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 the 0.05 level 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 a list of formulas.)

(a) State the null hypothesis H and the alternative hypothesis H. O P H : 1 X S P H 1 : 0 (b) Determine the type of test statistic to use. (Choose one) 0=0 030 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0*0 00 X ? (d) Find the two critical values at the 0.05 level of significance. (Round to three or more decimal places.) [ and (e) Can we support the claim that the mean completion time of Fundash is not equal to the mean completion time of Coolsprint? Yes ONo