Sheila Smith, the manager of a large resort’s main hotel, has been receiving complaints from some guests that they are not being provided with prompt service upon approaching the front desk. In particular, she is concerned that desk staff might be providing female guests with less prompt service than their male counterparts. In observing a sample of 34 male guests, she finds it takes an average of 15.2 seconds, with a standard deviation of 5.9 seconds, for them to be greeted after their arrival at the front desk. For a sample of 39 female guests, the mean and standard deviation are 17.4 seconds and 6.4 seconds, respectively. Assuming the population standard deviations to be equal, use the 0.05 level of significance in examining whether the population mean time for serving female guests might actually be no greater than that for serving male guests. Using the appropriate statistical table, what is the most accurate statement we can make about the p-value for the test?
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