Question

For the following hypothesis test, determine the null and alternative hypotheses. Also, classify the hypothesis test as two-tailed, left-tailed, or right-tailed. The mean length of imprisonment for motor-vehicle theft offenders in this country is 22.1 months. A hypothesis test is to be performed to determine whether the mean length of imprisonment for motor-vehicle theft offenders in this city differs from the national mean of 22.1 months.

Choose the correct null and alternative hypotheses below.
A. H0: μ = 22.1 months
Ha: μ > 22.1 months
B. H0: μ = 22.1 months
Ha: μ 22.1 months
C. H0: μ = 22.1 months
Ha: μ < 22.1 months
D. H0: μ > 22.1 months
Ha: μ = 22.1 months
E. H0: μ 22.1 months
Ha: μ = 22.1 months
F. H0: μ = 22.1 months
Ha: μ > 22.1 months
Which of the following is the correct classification of the hypothesis test?
A. Two-tailed
B. Left-tailed
C. Right-tailed

Answer 1

Option B:

`H_0: \mu = 22.1`

`H_a: \mu \\eq 22.1`

Classification:

The hypothesis test is Two-tailed.

Explanation:

The mean length of imprisonment for motor-vehicle theft offenders in this country is 22.1 months.

This means that the null hypothesis is that the mean is of 22.1 months, that is:

`H_0: \mu = 22.1`

A hypothesis test is to be performed to determine whether the mean length of imprisonment for motor-vehicle theft offenders in this city differs from the national mean of 22.1 months.

At the alternate hypothesis, we test if this mean is different of 22.1, that is:

`H_a: \mu \\eq 22.1`

Which means that the answer is given by option b).

Which of the following is the correct classification of the hypothesis test?

We test if the mean is different from a value, which means that the hypothesis test is Two-tailed.