Question

Medicare would like to test if the average monthly rate for one-bedroom assisted-living facility is different from $3,300. Suppose that you collect sample information and, based on the hypothesis test, determine that the z test statistic is equal to 1.98 while the critical value of z is 2.05. How would you state the conclusion?

Answer 1

We fail to reject our null hypothesis and conclude that there is not sufficient evidence to conclude that the average monthly rate for one-bedroom assisted-living facility is different from $3,300.

Explanation:

We are given that critical value of z=2.05

z test statistic=1.98

As we are testing that whether the the average monthly rate for one-bedroom assisted-living facility is different from $3,300, so this leads to two tailed hypothesis test as hypothesis are

Null hypothesis:μ=3300

Alternative hypothesis:μ≠3300.

The critical region in case of two tailed hypothesis test is

`|z|>z_{(\alpha )/(2) }`

1.98>2.05 (which is not true)

So, the test statistic don't lie in rejection region, thus we don't reject our null hypothesis and conclude that there is insufficient evidence to conclude that the average monthly rate for one-bedroom assisted-living facility is different from $3,300.