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 fit test and the sample size. In each case, decide whether Assumptions \(1\) and \(2\) for using that test are satisfied.

Sample size: \(n=50\)

Relative frequencies: \(0.22, 0.22, 0.25, 0.30, 0.01\).

Short answer

The assumption\(1\) is not satisfied and assumption\(2\) is satisfied.

Step-by-step solution

Step 1. Given information

Consider the sample size \(n=50\),

Relative frequencies \(0.22, 0.22, 0.25, 0.30, 0.01\)

Step 2. Calculation

Consider the relative frequencies \(p=0.22, 0.22, 0.25, 0.30, 0.01 \)

Then, determine the expected frequencies

\(np=50(0.22, 0.22, 0.25, 0.30, 0.01)\)

\(np=11,11,12.5,15,0.5\).

The number of expected frequencies less than \(1=1\) (assumption \(1\) is not satisfied)

The number of expected frequencies less than \(5=1\)

The percentage of expected frequencies less than \(5\) is \(=\frac{1}{5}(100)\)

\(=20%\) (assumption\(2\) satisfied)

Hence, the assumption\(1\) is not satisfied and assumption\(2\) is satisfied.