Chapter 11.1, Problem 20E

To determine

To find: The chi-square statistic.

Answer to Problem 20E

The chi-square statistic is $\frac{{\left(18-25\right)}^2}{25}+\frac{{\left(22-25\right)}^2}{25}+\frac{{\left(39-25\right)}^2}{25}+\frac{{\left(21-25\right)}^2}{25}$

Explanation of Solution

Given:

The table is:

Quadratic	Count
1	18
2	22
3	39
4	21

Formula used:

The formula to compute the test statistic is

  ${\chi }^2={\displaystyle \sum {\left(O-E\right)}^2/E}$

Calculation:

The calculation for test statistic could be done as:

Observed value (O)	Expected value (E)
18	0.25(100) = 25
22	0.25(100) = 25
39	0.25(100) = 25
21	0.25(100) = 25

The test statistic is:

  $\begin{array}{c}{\chi }^2={\displaystyle \sum \frac{{\left(O-E\right)}^2}{E}}\\ =\frac{{\left(18-25\right)}^2}{25}+\frac{{\left(22-25\right)}^2}{25}+\frac{{\left(39-25\right)}^2}{25}+\frac{{\left(21-25\right)}^2}{25}\end{array}$

Thus, the test statistic is $\frac{{\left(18-25\right)}^2}{25}+\frac{{\left(22-25\right)}^2}{25}+\frac{{\left(39-25\right)}^2}{25}+\frac{{\left(21-25\right)}^2}{25}$

Thus, the correct option is (a).