We want to conduct a hypothesis test of the claim that the population mean daily profit of a convenience store is more than

$516$ dollars. So$,$ we record the daily profit for a random sample of days. The sample has a mean of $521$ dollars and a

standard deviation of $77$ dollars.

For each of the following sampling scenarios, choose an appropriate test statistic for our hypothesis test on the population

mean. Then calculate that statistic. Round your answers to two decimal places.

$($a$)$ The sample has size $10,$ and it is from a population with a distribution about which we know very little.

$z=$

$t=$

It is unclear which test statistic to use.

$($b$)$ The sample has size $85,$ and it is from a non$-$normally distributed population with a known standard deviation of $76.$

$z=$

$t=$

It is unclear which test statistic to use.