Q.1.3 - The Practice of Statistics for AP

Question

Calculate the chi-square statistic for Joey’s sample. Show your work 

Step-by-Step Solution

Answer

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

Step 1: Given Information

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.

Step 2: Explanation

The formula to compute the test statistic is

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

The calculation for test statistics could be done as:

$\begin{array}{|ccccc|}\hline \text{ Observed value }& \text{ Expected value }& (O-E)& (O-E{)}^2& (O-E{)}^2/E\\ 12& 10.58& 1.42& 2.0164& 0.191\\ 7& 10.58& -3.58& 12.816& 1.211\\ 13& 6.9& 6.1& 37.21& 5.393\\ 4& 5.9& -2.9& 8.41& 1.219\\ 8& 5.52& 2.48& 6.1504& 1.114203\\ 2& 5.52& -3.52& 12.3904& 2.244638\\ \hline\end{array}$

The test statistic is:

${\chi }^2=\sum \frac{(O-E{)}^2}{E}$

    $=11.3724$