In Exercises 10.25-10.30, hypothesis tests are proposed. For each

hypothesis test,

a. identify the variable.

b. identify the two populations,

c. determine the null and alternative hypotheses.

d. classify the hypothesis test as two-tailed, left-tailed, or right-tailed.

Driving Distances.Data on household vehicle miles of travel (VMT) are compiled annually by the Federal Highway Administration and are published in National Household Travel Survey. Summary of Travel Trends. A hypothesis test is to be performed to decide whether a difference exists in last year's mean VMT for households in the Midwest and South.

We have been a proposed a hypothesis.

A hypothesis test is to be performed to decide whether a difference exists in last year's mean VMT for households in the Midwest and South.

A variable is an attribute or a characteristic that can be measured. The value of the variable may differ for each and every unit. That is, a variable is defined as the characteristic which is recorded for each case.

In the given study last year's vehicle mile of travel (VMT) is noted. So the variable is last year's vehicle mile of travel (VMT).

The population includes all the individuals of interest that are being examined. In other words, the collection of all people, items, or objects that are required for a specific study is defined as the population.

The given study involves measuring last year's vehicle mile of travel (VMT) for households in the Midwest and South.

So the two populations are households in the Midwest and the households in South.

Let us assume ${\mu }_1$denotes last year's mean VMT for households in the Midwest and ${\mu }_2$last year's mean VMT for households in the South.

The Null Hypothesis is defined as

$H_0:$There is no significant difference between the last year's mean VMT for households in the Midwest and South.

$H_0:{\mu }_1={\mu }_2$

The Alternative Hypothesis is defined as

$H_a:$There is significant difference between the last year's mean VMT for households in the Midwest and South.

$H_a:{\mu }_1\ne {\mu }_2$

As our alternative hypothesis suggest that the mean of the first population is not equal to the mean of the second population.

So the hypothesis can be classified as a two-tailed test.