A botanist for a large rose farm is told that the company currently averages $9$ thousand roses per year. The company hires her to work as an outside consultant in order to increase their annual rose production.

The hypotheses are given.

H$0$: $=9$ thousand

Ha: $>9$ thousand

$($a$)$

Define what a Type I error is in the context of this problem.

The company concludes that it produces more than $9$ thousand roses per year, when it really is producing $9$ thousand roses.

The company concludes that it produces $9$ thousand roses per year on average, when it is actually producing more.

The company concludes that it produces less than $9$ thousand roses per year, when it really is producing $9$ thousand roses.

The company concludes that it produces $9$ thousand roses per year, when it really is producing less.

$($b$)$

State the consequences of making a Type I error in the context of this problem.

The company fires the consultant because it thinks annual production has stayed the same in spite of the consultant's work, when really it has increased.

The company fires the consultant because it thinks annual production has decreased in spite of the consultant's work, when really it has stayed the same.

The company rewards the consultant for increasing annual production, when really production has decreased.

The company rewards the consultant for increasing annual production, when really production has stayed the same.