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Chapter 12: Q. 12.69 (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.

12.69 four and five

Short Answer

Expert verified

Ans: The maximum number of expected frequencies that can be less than 5 by using Assumption 2 is 4

Step by step solution

01

Step 1. Given information.

given,

four and five

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 sample
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 5 . Therefore, there are 20(=4×5)expected frequencies.

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

localid="1651856327095" 20%of20=20100×20=4

Thus, the maximum number of expected frequencies that can be less than 5 by using Assumption 2 is 4.

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Most popular questions from this chapter

In each of Exercises 12.11-12.16, we have given the relative frequencies for the null hypothesis of a chi-square goodness-of-fir text and the sample size. In each case, decide whether Assumptions 1 and 2 for using that text are satisfied.

Sample size : n= 50.

Relative frequencies: 0.22 , 0.21 , 0.25 , 0.30 , 0.02.

Studies have shown that a positive association exists between educational level and annual salary; in other words, people with more education tend to make more money.
a. Does this finding mean that more education causes a person to make more money? Explain your answer.
b. Do you think there is a casual relationship between educational level and annual salary? Explain your answer.

For a χ2-curve with df=4, determine

a. χ0.0052

b.χ0.012

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For single-unit occupied housing units:


OwnerRenterTotal
Full-basement22,9873,30126,288
Partial-basement7,5169908,506
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a. How many have crawl spaces?

b. How many are owner occupied?

c. How many are rented and have full basements?

d. How many have a basement?

e. How many are either owner occupied or have a concrete slab?

Education of Prisoners. In the article "Education and Correctional Populations" (Bureau of Justice Statistics Special Report, NCJ 195670), C. Harlow examined the educational attainment of prisoners by type of prison facility. The following contingency table was adapted from Table 1 of the article. Frequencies are in thousands, rounded to the nearest hundred.


StateFederalLocalTotal
8th grade or less149.910.666.0226.5
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How many prisoners

a. are in state facilities?

b. have at least a college education?

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d. are in federal facilities or have at most an 8th-grade education? e. in local facilities have a postsecondary educational attainment

f. who have a postsecondary educational attainment are in local facilities?

g. are not in federal facilities?
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