A factory manager claims that the average daily output of machines is greater than $200$ units. To test this claim, a random sample of $30$ machines shows a mean output of $206$ units per day. The population standard deviation is known to be $12$ units. At the $0.10$ level of significance, is there sufficient evidence to support the manager’s claim?

A $t$-test should be used instead of a $z$-test since the sample size is small.

There is insufficient evidence to support the claim that the average output is more than $200$ units.

There is sufficient evidence to conclude that the average output is less than $200$ units.

There is sufficient evidence to support the claim that the average output is more than $200$ units.