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 210 Fundash runners and 235 Coolsprint runners. (Consider these as random samples of the Fundash and Coolspring runners.) The 210 Fundash runners complete the course with a mean time of 75.5 minutes and a standard deviation of 3.9 minutes. The 235 Coolsprint runners complete the course with a mean time of 74.7 minutes and a standard deviation of 3.5 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 0.10 level of significance, is there enough evidence to support the claim that the mean completion time, μ₁, of Fundash is not equal to the mean completion time, μ₂, of Coolsprint? Perform a two-tailed test. Then complete the parts below.

(a) State the null hypothesis H0 and the alternative hypothesis H₁.
(b) Determine the type of test statistic to use.
(c) Find the value of the test statistic. (Round to three or more decimal places.)
(d) Find the critical value at the 0.01 level of significance. (Round to three or more decimal places.)