Q.1.2 - The Practice of Statistics for AP

Question

Calculate the expected count for each color, assuming that the company’s claim is true. Show your work. 

Step-by-Step Solution

Answer

The expected count is

$\begin{array}{|ll|}\hline \text{ Blue }& 46(0.23)=10.58\\ \text{ Orange }& 46(0.23)=10.59\\ \text{ Green }& 46(0.15)=6.9\\ \text{ Yellow }& 46(0.15)=6.9\\ \text{ Red }& 46(0.12)=5.52\\ \text{ Brown }& 46(0.12)=5.52\\ \hline\end{array}$

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 expected count could be computed as:

$\begin{array}{|ll|}\hline \text{ Blue }& 46(0.23)=10.58\\ \text{ Orange }& 46(0.23)=10.59\\ \text{ Green }& 46(0.15)=6.9\\ \text{ Yellow }& 46(0.15)=6.9\\ \text{ Red }& 46(0.12)=5.52\\ \text{ Brown }& 46(0.12)=5.52\\ \hline\end{array}$