Chapter 11.2, Problem 53E

a)

To determine

To state the null and alternative hypotheses.

Answer to Problem 53E

  $H_0$ : There is no difference in the improvement rate of the two treatment groups.

  $H_a$ : There is difference in the improvement rate of the two treatment groups.

Explanation of Solution

Given:

Claim: We can test the hypothesis of “no difference” in the effectiveness of the treatment in two-ways.

Calculation:

The null and alternative hypotheses:

  $H_0$ : There is no difference in the improvement rate of the two treatment groups.

  $H_a$ : There isdifference in the improvement rate of the two treatment groups.

b)

To determine

To state the conclusion.

Answer to Problem 53E

There is no convincing evidence that there is a difference in the improvement rate of the two treatment groups.

Explanation of Solution

Given:

Calculation:

The p-value = 0.570. Therefore, we can say, there is 57% chance of obtaining the sample results or more extreme when there is no difference in the improvement rate of the two treatment groups.

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

Conclusion: There is no convincing evidence that there is a difference in the improvement rate of the two treatment groups.

c)

To determine

To compare chi-square test and z-test.

Answer to Problem 53E

The p-value of chi-square test and z-test is same so, conclusion based on two tests are same.

Explanation of Solution

Given:

Calculation:

The p-value = 0.570. The p-value of chi-square test and z-test is same. Therefore, conclusion based on two tests are same.

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

Also, chi-square test statistic = 0.322 and z-test statistic = -0.57

We know the property that square of z becomes the chi-square.

So, $z^2={\left(-0.57\right)}^2=0.322={\chi }^2$

This property is satisfied.