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= 50.

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

Short answer

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

In assumption 2 ,

Number of expected frequencies less than 5 = 0

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

Both the assumptions are satisfied.

Step-by-step solution

Step 1. Given 

The sample size is n= 50

Step 2. Assumption 1 

Relative frequency	Expected frequency
( p)	( np )
0.22	11
0.21	10.5
0.25	12.5
0.30	15
0.02	1

All the expected frequencies are $\ge$1.

$\therefore$Assumption 1 is satisfied .

Step 3. Assumption 2

Number of expected frequencies less than 5 = 0

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

$\therefore$Assumption 2 is satisfied.

$\therefore$Both the assumptions are satisfied.