Chapter 11.1, Problem 1.3CYU

To determine

To find: The chi-square statistic.

Answer to Problem 1.3CYU

The expected counts are 10.58, 10.59, 6.9, 6.9, 5.52 and 5.52 respectively.

Explanation of Solution

Given:

The number of blue, orange, green, yellow, red and brown candies are 12, 7, 13, 4, 8 and 2 respectively.

The proportions are 23%, 15% and 12% respectively.

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	Expected value	$\left(O-E\right)$	${\left(O-E\right)}^2$	${\left(O-E\right)}^2/E$
12	10.58	1.42	2.0164	0.191
7	10.58	-3.58	12.816	1.211
13	6.9	6.1	37.21	5.393
4	6.9	-2.9	8.41	1.219
8	5.52	2.48	6.1504	1.114203
2	5.52	-3.52	12.3904	2.244638
				${\displaystyle \sum {\left(O-E\right)}^2/E}=11.3724$

The test statistic is:

  $\begin{array}{c}{\chi }^2={\displaystyle \sum \frac{{\left(O-E\right)}^2}{E}}\\ =11.3724\end{array}$

Thus, the test statistic is 11.3724.