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Chapter 12: Q. 12.72 (page 510)

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.

12.72 four and three

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given information.

given,

four and three

02

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.
03

Step 3. Now,

According to the given information, the number of possible values for the first variable is 4 and the number of possible values for the second variable is 3 . Therefore, there are 12(=4×3)expected frequencies.

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

20%of12=20100×12=2.4≈2

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

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12.73 two and two

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