he manager of a large resort hotel, has been receiving complaints from some guests that they are not being provided with prompt service upon approaching the front desk. In particular, he is concerned...

he manager of a large resort hotel, has been receiving complaints from some guests that they are not being provided with prompt service upon approaching the front desk. In particular, he is concerned that the desk staff might be providing female guests with less prompt service than their male counterparts. For a sample of
35
male guests, he found that
it takes an average of
15.2
seconds, with a standard deviations5.9
seconds for them to be greeted after their arrival at the front desk. For a sample of
37
female guests, the mean and standard deviation are
17.4
seconds and
6.4
seconds, respectively. Assuming the two population are independent and the population variances are equal, hypotheses examine whether the population mean time for serving female guests might actually be greater than that of serving male-guests. Suppose that the pooled variance is 37.9729.

The test statistic is