Question

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

In assumption 1 , All the expected frequencies are $\ge$1.

In assumption 2 ,

Number of expected frequencies less than 5 = 1

Percentage of expected frequencies less than 5 =$\frac{1}{4}\times 100=25>20\%$

Step-by-step solution

Step 1. Given  

The sample size is n= 100

Step 2. Assumption 1  

Relative frequency	Expected frequency
( p )	( np )
0.44	44
0.25	25
0.30	30
0.01	1

All the expected frequencies are $\ge$1.

$\therefore$Assumption 1 is satisfied .

Step 3. Assumption 2 

Number of expected frequencies less than 5 = 1

Percentage of expected frequencies less than 5 = $\frac{1}{4}\times 100=25>20\%$

Assumption 2 is not satisfied.