Hypothesis testing and type error question?

Question

1. A homeowner is getting carpet installed. The installer is charging her for 250 square feet. She thinks this is more than the actual space being carpeted. She asks a second installer to measure the space to confirm her doubt. Write the null hypothesis H_o and the alternative hypothesis H_a.

Answer 1

Step 1:

A home owner want to install carpet to his house.

The installer charging her for 250 square feet.

But she thinks that the area is less than 250 square feet.

Null hypothesis :

One of these statements must become the null hypothesis , and the other should be the alternate hypothesis.

The null hypothesis contains equality.

So for the above, the null hypothesis H₀ : x = 250.

Step 2:

Alternate hypothesis :

The statement that does not contain equality is the alternative hypothesis.

So for the above, the alternate hypothesis H_a : x < 250.

Solution :

Null hypothesis : H₀ : x = 250.

Alternate hypothesis H_a : x < 250.