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Chapter 12: Q. 12.71 (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.

12.71 two and three

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given information.

given,

two 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 2 and the number of possible values for the second variable is 3 . Therefore, there are 6(=2×3)expected frequencies.

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

20%of20=20100×6=1.2

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

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Most popular questions from this chapter

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Job Satisfaction. A CNN/USA TODAY poll conducted by Gallul asked a sample of employed Americans the following question: "Which do you enjoy more, the hours when you are on your job, or the hours when you are not on your job?" The responses to this question were cross-tabulated against several characteristics, among which were gender, age, type of community, educational attainment, income, and type of employer. The data are provided on the WeissStats site. In each of Exercises 12.87-12.92, use the technology of your choice to decide, at the 5% significance level, whether an association exists between the specified pair of variables.

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