Q. 2.1 - The Practice of Statistics for AP

Question

Let’s continue our analysis of Joey’s sample of M&M’S Peanut Chocolate Candies from the previous Check Your Understanding (page 681). Here is the brief intro of the question:

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. 

1. Confirm that the expected counts are large enough to use a chi-square distribution. Which distribution (specify the degrees of freedom) should we use?

Step-by-Step Solution

Answer

Yes we can use use Chi-square distribution here.

The degree of freedom here is $5.$

Given information

We are expected about 23% of the candies are blue and orange, 15% each of green and yellow, and 12% each of red and brown.

Joey buys candies and counted the colors of the candies in his sample: 12 blue, 7 orange, 13 green, 4 yellow, 8 red, and 2 brown.

Explanation

We are given that the frequencies are varing across different observations therefore we can use Chi-square distribution.

Also the no. of different objects are $n=6$.

Therefore the degree of freedom is $n-1=5$.