An auditor for a government agency was assigned the task of evaluating reimbursement for office visits to physicians paid by Medicare. The audit was conducted on a sample of $75$ reimbursements, with the following results:

$$ In $17$ of the office visits, there was an incorrect amount of reimbursement.

$$ The amount of reimbursement was x$=$$$93\mathrm{.}70$ S$=$$$34\mathrm{.}55$

A$.$ a$.$ At the $0\mathrm{.}05$ level of significance, is there evidence that the population mean reimbursement was less than $$100?$