Q.1.3 - The Practice of Statistics for AP

Question

Mars, Inc., reports that their M&M’S Peanut Chocolate Candies are produced according to the following color distribution: 23% each of blue and orange, 15% each of green and yellow, and 12% each of red and brown. Joey bought a bag of Peanut Chocolate Candies and counted the colors of the candies in his sample: 12 blue, 7 orange, 13 green, 4 yellow, 8 red, and 2 brown.

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

Step-by-Step Solution

Answer

The test statistic is  11.3724

Step 1 Given Information

Given that 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 Calculation for Test statistic

The formula to calculate the test statistic is

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

The test statistic is:

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

=11.372

Thus, the test statistic is $11.3724$.