Chapter 26, Problem 16E

a)

To determine

To find the degrees of freedom.

Answer to Problem 16E

The degrees of freedom are 2

Explanation of Solution

Given:

  

Formula:

  $df=(r-1)(c-1)$

The number of rows = r = 2

The number of columns = c = 3

Therefore, the degrees of freedom are:

  $df=(2-1)\times (3-1)=2$

b)

To determine

To find the smallest expected count.

Answer to Problem 16E

The smallest expected count is 21.847

Explanation of Solution

Given:

  

Formula:

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

The smallest count is 190. Therefore, expected count is,

  $E=\frac{144\times 115}{758}=21.847$

c)

To determine

To check the assumptions and conditions.

Answer to Problem 16E

All the conditions satisfied.

Explanation of Solution

Given:

  

There are three main conditions of Chi-square test:

Counts, Independent and expected counts are at least 5.

The data has given counts so the condition of counts satisfied.

Assuming that articles are independent, so condition of independent is satisfied.

The smallest expected count is larger than 5 so all the conditions satisfied.