Question

In each of the given Exercises, we have given the number of possible values for two variables of a population. For each exercise, determine the maximum number of expected frequencies that can be less than 5 in order that Assumption 2 of Procedure 12.2 on page 506 to be satisfied. Note: The number of cells for a contingency table with m rows and n columns is m⋅n.

12.71 two and three

Short answer

Ans: The maximum number of expected frequencies that can be less than 5 by using Assumption 2 is 1.2.

Step-by-step solution

Step 1. Given information.

given,

two and three

Step 2. First, determine the maximum number of expected frequencies that can be less than 5 by using Assumption 2. 

Assumption:

1. All expected frequencies are at least 1.
2. At most 20% of the expected frequencies are less than 5.
3. All the selected samples should be a simple random samples.

Step 3. Now,

According to the given information, the number of possible values for the first variable is 2 and the number of possible values for the second variable is 3 . Therefore, there are $6(=2\times 3)$expected frequencies.

The maximum number of expected frequencies that can be less than 5, by using Assumption 2 is,

$$\begin{gathered} 20\%of20=\frac{20}{100}\times 6 \\ =1.2 \end{gathered}$$

Hence, the maximum number of expected frequencies that can be less than 5 by using Assumption 2 is 1.2.