Chapter 8.1, Problem 13E

For each conjecture, state the null and alternative hypotheses.

a. The average weight of dogs is 15.6 pounds.

b. The average distance a person lives away from a toxic waste site is greater than 10.8 miles.

c. The average farm size in 1970 was less than 390 acres.

d. The average number of miles a vehicle is driven per year is 12,603.

e. The average amount of money a person keeps in his or her checking account is less than $24.

To determine

To state: The null and alternative hypotheses.

Answer to Problem 13E

Null hypothesis:

$H_0:\mu =15.6\text{pounds}$

Alternative hypothesis:

$H_1:\mu \ne 15.6\text{pounds}$

Explanation of Solution

Given info:

The average weight of dogs is 15.6 pounds.

Justification:

Null hypothesis:

A statement about population parameter which is equal to the value mentioned in claim value, which is denoted by $H_0$. The population parameter may be mean, standard deviation, proportion, variance, etc. The possible symbols used in the null hypothesis would be $\le ,\ge$ or =.

Alternative hypothesis:

It is opposite to the null hypothesis. That is, it differs from the null hypothesis. The possible symbols used in the alternative hypothesis would be <,>, or ≠. It is denoted by $H_1$.

Here, the claim is that the average weight of dogs is 15.6 pounds. This can be written as $\mu =15.6\text{pounds}$. The complement of the claim is, $\mu \ne 15.6\text{pounds}$. Therefore, the null and alternative hypotheses are given below:

Null hypothesis: $H_0:\mu =15.6\text{pounds}$

Alternative hypothesis: $H_1:\mu \ne 15.6\text{pounds}$

To determine

To state: The null and alternative hypotheses.

Answer to Problem 13E

Null hypothesis:

$H_0:\mu =10.8\text{miles}$

Alternative hypothesis:

$H_1:\mu >10.8\text{miles}$

Explanation of Solution

Given info:

The average distance a person lives away from a toxic waste site is greater than 10.8 miles.

Justification:

Here, the claim is that the average distance a person lives away from a toxic waste site is greater than 10.8 miles. This can be written as $\mu >10.8\text{miles}$. The complement of the claim is, $\mu =10.8\text{miles}$. Therefore, the null and alternative hypotheses are given below:

Null hypothesis: $H_0:\mu =10.8\text{miles}$

Alternative hypothesis: $H_1:\mu >10.8\text{miles}$

To determine

To state: The null and alternative hypotheses.

Answer to Problem 13E

Null hypothesis:

$H_0:\mu =390\text{acres}$

Alternative hypothesis:

$H_1:\mu <390\text{acres}$

Explanation of Solution

Given info:

The average farm size in 1970 was less than 390 acres.

Justification:

Here, the claim is that the average farm size in 1970 was less than 390 acres. This can be written as $\mu <390\text{acres}$. The complement of the claim is, $\mu =390\text{acres}$. Therefore, the null and alternative hypotheses are given below:

Null hypothesis: $H_0:\mu =390\text{acres}$

Alternative hypothesis: $H_1:\mu <390\text{acres}$

To determine

To state: The null and alternative hypotheses.

Answer to Problem 13E

Null hypothesis:

$H_0:\mu =12,603$

Alternative hypothesis:

$H_1:\mu \ne 12,603$

Explanation of Solution

Given info:

The average number of miles a vehicle is driven per year is 12,603.

Justification:

Here, the claim is that the average number of miles a vehicle is driven per year is 12,603. This can be written as $\mu =12,603$. The complement of the claim is, $\mu \ne 12,603$. Therefore, the null and alternative hypotheses are given below:

Null hypothesis: $H_0:\mu =12,603$

Alternative hypothesis: $H_1:\mu \ne 12,603$

To determine

To state: The null and alternative hypotheses.

Answer to Problem 13E

Null hypothesis:

$H_0:\mu =\$24$

Alternative hypothesis:

$H_1:\mu <\$24$

Explanation of Solution

Given info:

The average amount of money a person keeps in his or her checking account is less than $24.

Justification:

Here, the claim is that the average amount of money a person keeps in his or her checking account is less than $24. This can be written as $\mu <\$24$. The complement of the claim is, $\mu =\$24$. Therefore, the null and alternative hypotheses are given below:

Null hypothesis: $H_0:\mu =\$24$

Alternative hypothesis: $H_1:\mu <\$24$