Q. 2.2 - 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).

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. 

2. Sketch a graph like Figure 11.4 that shows the P-value.

Step-by-Step Solution

Answer

The p-value can be visualized (area shaded in blue) as follows:

Given

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.  

Formulation

In order to calculate the p value we need to calculate the chi-square statistics.

The formula for chi-square statistics is:

${𝓧}^2=\sum _i\frac{{\left(O_i-E_i\right)}^2}{E_i}$

Upon putting the value in above formula and simplifying we get,

${𝓧}^2=11.1516$

The p-value

The p-value is depicted in the following figure (shaded in light blue) as follows: