Chapter 11.2, Problem 52E

a.

To determine

To find: The test that is to be used in the provided case.

Answer to Problem 52E

Chi-square test of homogeneity.

Explanation of Solution

Given:

The output is:

  

Here, two-way table has been computed for the one qualitative variable of two sample. Thus, chi-square test of homogeneity should be used here.

b.

To determine

To state: The appropriate null and alternative hypotheses for the provided test.

Explanation of Solution

Calculation:

The appropriate null and alternative hypotheses for the provided test could be written as:

  $\begin{array}{l}{H}_0:\text{ There is no relationship between two variables}\\ H_a:\text{ There is a relationship between two variables}\end{array}$

c.

To determine

To check: If the required conditions to conduct the test are met or not.

Explanation of Solution

Here, in this case following conditions are following:

1. Sample is chosen random.
2. All the expected counts are above 5.
3. The size of the sample is 10% smaller than the population.

Thus, it could be said that the required conditions are fulfilled.

d.

To determine

To interpret: The P -value and draw the conclusion.

Explanation of Solution

If no relationship exists between the variables then the likelihood of having same or extreme sample is 0.01%

Conclusion:

The p -value < 0.05. The null hypothesis is rejected. Thus, at 5% significance level there is sufficient evidence to reject the claim that there is an association between the two variables.