Chapter 23, Problem 23.9CYS

To determine

To find: The hypotheses that has to be tested.

Answer to Problem 23.9CYS

Correct answer:

The hypotheses to be tested are $H_0:p_9=p_{12}\text{ versus }{H}_a:p_9>p_{12}$.

Explanation of Solution

Reason for the correct answer:

In the given situation, there is evidence that the proportion of 12^th graders who eat breakfast daily is lower than the proportion of 9^th-graders eating breakfast daily is tested.

Hence, option (b) is correct.

Reason for the incorrect answer:

Option (a) and Option (c) are incorrect, because the proportion of 12^th graders who eat breakfast daily is lower than the proportion of 9^th-graders eating breakfast daily is tested.

Conclusion:

The test hypotheses for the proportion of 12^th graders who eat breakfast daily is lower than the proportion of 9^th-graders eating breakfast daily is $H_0:p_9=p_{12}\text{ versus }{H}_a:p_9>p_{12}$.

Statistics Concept Introduction

Introduction:

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.

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 $H_a$