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Chapter 12: Q. 12.16 (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= 100.

Relative frequencies: 0.44 , 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 =14×100=25>20%

Step by step solution

01

Step 1. Given  

The sample size is n= 100

02

Step 2. Assumption 1  

Relative frequency
Expected frequency
( p )( np )
0.4444
0.2525
0.3030
0.011

All the expected frequencies are ≥1.

∴Assumption 1 is satisfied .

03

Step 3. Assumption 2 

Number of expected frequencies less than 5 = 1

Percentage of expected frequencies less than 5 = 14×100=25>20%

Assumption 2 is not satisfied.

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