Chapter 26, Problem 34E

a)

To determine

To state which test would be appropriate for given situation.

Answer to Problem 34E

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 Homogeneity would be appropriate to use.

b)

To determine

To state null and alternative hypotheses.

Answer to Problem 34E

  $H_0$ : The type of illegal activity is the same on the full moon as not on the full moon.

  $H_a$ : The type of illegal activity is different on the full moon.

Explanation of Solution

Given:

  

The null and alternative hypotheses:

  $H_0$ : The type of illegal activity is the same on the full moon as not on the full moon.

  $H_a$ : The type of illegal activity is different on the full moon.

c)

To determine

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

Answer to Problem 34E

The condition for chi-square test is not satisfied.

Explanation of Solution

Given:

  

Formula:

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

The smallest count is 2. Therefore, expected count corresponding to it is,

  $E=\frac{66\times 5}{129}=2.5581$

The expected count is 2.5581 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.