Chapter 26, Problem 33E

a)

To determine

To state which test would be appropriate for given situation.

Answer to Problem 33E

Chi-square test for Homogeneity.

Explanation of Solution

Given:

  

When we want to check whether the distribution of one variable is the same in multiple group then we use Chi-square test of Homogeneity.Also, there is count given for two variables. Hence, Chi-square test for Homogeneitywould be appropriate to use.

b)

To determine

To state null and alternative hypotheses.

Answer to Problem 33E

  $H_0$ : The grade distribution is the same for all teachers.

  $H_a$ : The grade distribution is different among teachers.

Explanation of Solution

Given:

  

The null and alternative hypotheses:

  $H_0$ : The grade distribution is the same for all teachers.

  $H_a$ : The grade distribution is different among teachers.

c)

To determine

To find the expected count and explain why chi-square test is not appropriate.

Answer to Problem 33E

The condition for chi-square test is not satisfied.

Explanation of Solution

Given:

  

Formula:

  $E=\frac{Rowtotal\times Columntotal}{Total}$

The smallest count is 1. Therefore, expected count corresponding to it is,

  $E=\frac{32\times 4}{72}=1.7777$

The expected count is 1.7777 which is less than 5. Therefore, condition for chi-square test is not satisfied. Hence, it is not appropriate to use Chi-square test of Homogeneity.