Chapter 9, Problem 67CP

H₀ or H_a? For each of the following hypotheses, explain whether it is a null hypothesis or an alternative hypothesis:

1. a. For females, the population mean on the political ideology scale is equal to 4.0.
2. b. For males, the population proportion who support the death penalty is larger than 0.50.
3. c. The diet has an effect, the population mean change in weight being less than 0.
4. d. For all Subway (submarine sandwich) stores worldwide, the difference between sales this month and in the corresponding month a year ago has a mean of 0.

To determine

Identify whether the statement is null hypothesis or alternative hypothesis.

Answer to Problem 67CP

The given statement is null hypothesis.

Explanation of Solution

The given statement is that the population mean on the political ideology scale for female is equal to 4.

Null hypothesis:

It is a statement in which the parameter takes certain value and it is denoted as ${\text{H}}_0$. The population parameter may be mean, standard deviation, proportion, variance, and so forth.

Alternative hypothesis:

If the statement tells that the parameter falls in alternative range of values then it is termed as alternative hypothesis. It is denoted as ${\text{H}}_a$ and generally tells about some claim. The possible symbols used in the alternative hypothesis would be <,>, or ≠.

The value in the hypothesis generally represents no effect then the value in alternative hypothesis represents an effect of some type.

Here, the value in hypothesis represents no effect. That is, the population mean on the political ideology scale for female is equal to 4. Hence, the statement is null hypothesis.

To determine

Identify whether the statement is null hypothesis or alternative hypothesis.

Answer to Problem 67CP

The given statement is Alternative hypothesis.

Explanation of Solution

It is given that the population proportion who support the death penalty is larger than 0.50.

Here, the hypothesis represents the greater than or larger than $(>)$ term which represents the claim and denotes the effect of some type. Hence, the statement is alternative hypothesis.

To determine

Identify whether the statement is null hypothesis or alternative hypothesis.

Answer to Problem 67CP

The given statement is Alternative hypothesis.

Explanation of Solution

It is given that the diet has an effect and the population mean change in weight is less than 0.

Here, the hypothesis represents the less than $(<)$ term which represents the claim denotes the effect of some diet. Hence, the statement is alternative hypothesis.

To determine

Identify whether the statement is null hypothesis or alternative hypothesis.

Answer to Problem 67CP

The given statement is null hypothesis.

Explanation of Solution

The given statement is that the difference between sales at current month and in the corresponding month a year ago is 0.

The value in the hypothesis generally represents no effect then the value in alternative hypothesis represents an effect of some type.

Here, the value in hypothesis represents no effect. That is, the population mean difference between sales at current month and in the corresponding month a year ago, is equal to 0. Hence, the given statement is a null hypothesis.