Chapter 11, Problem T11.12SPT

a)

To determine

To explain the purpose of the random assignment in the design of this study.

Answer to Problem T11.12SPT

Random assignment helps to make unbiased result.

Explanation of Solution

Given:

The conditions of testing a chi-square test are important to make as result accurate. From that conditions, the condition of random assignment is most important. Because, the random assignment helps to make groups of each treatment as similar as possible and to eliminate the effect of any variables that are not included in the study.

b)

To determine

To state hypotheses.

Answer to Problem T11.12SPT

  $H_0$ : The true proportion of spouse abusers like the ones in the study who will be arrested within 6 months is the same for all three police responses.

  $H_a$ : The true proportion of spouse abusers like the ones in the study who will be arrested within 6 months is not same for all three police responses.

Explanation of Solution

Given:

Calculation:

The null and alternative hypotheses:

  $H_0$ : The true proportion of spouse abusers like the ones in the study who will be arrested within 6 months is the same for all three police responses.

  $H_a$ : The true proportion of spouse abusers like the ones in the study who will be arrested within 6 months is not same for all three police responses.

c)

To determine

To interpret the p-value.

Answer to Problem T11.12SPT

The p-value explains if all population probabilities are equal then the probability of obtaining a similar sample or more extreme is 7.96%.

Explanation of Solution

Given:

  ${\chi }^2=5.063$

P-value = 0.0796

Calculation:

The p-value explains if all population probabilities are equal then the probability of obtaining a similar sample or more extreme is 7.96%.

d)

To determine

To make a conclusion.

Answer to Problem T11.12SPT

There is not sufficient evidence to reject the claim of equal proportions in each group.

Explanation of Solution

Given:

  ${\chi }^2=5.063$

P-value = 0.0796

Calculation:

Decision: The p-value > 0.05, fail to reject H0.

Conclusion: There is not sufficient evidence to reject the claim of equal proportions in each group.