$6.$ The average undergraduate cost per tuition, fees, room, and board for all institutions last year

was $$26,025.$ A random sample of $40$ institutions of higher learning this year indicated that the

mean tuition, fees, room, and board for the sample was $$27,690,$ and the population standard

deviation is $$5492.$ At the $0\mathrm{.}05$ level of significance, is there sufficient evidence that the cost has

increased? $($Remember to follow the steps in hypothesis testing$)$