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.

12.74 six and seven

Short answer

Ans: The maximum number of expected frequencies that can be less than 5 by using Assumption 2 is 8.

Step-by-step solution

Step 1. Given information.

given,

six and seven

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 6 and the number of possible values for the second variable is 7. Therefore, there are $42(=6\times 7)$expected frequencies.

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

$$\begin{gathered} 20\%of42=\frac{20}{100}\times 42 \\ =8.4\approx 8 \end{gathered}$$

Hence, the maximum number of expected frequencies that can be less than 5 by using Assumption 2 is 8.