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Chapter 12: Q. 12.15 (page 491)

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 , 0.22 , 0.25 , 0.30 , 0.01.

Short Answer

Expert verified

In assumption 1 , All the expected frequencies are≥1.

In assumption 2 ,

Number of expected frequencies less than 5 = 1

Percentage of expected frequencies less than 5 = 15×100=20

Step by step solution

01

Step 1. Given information

The sample size is n= 50

02

Step 2. Assumption 1 

Relative frequencyExpected frequency
( p)( np )
0.2211
0.2211
0.2512.5
0.3015
0.010.5

expected frequencies are 0.5 < 1.

Assumption 1 is not satisfied .

03

Step 3. Assumption 2

Number of expected frequencies less than 5 = 1

Percentage of expected frequencies less than 5 = 15×100=20

∴Assumption 2 is satisfied.

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