Question

the expected proportions of colors of m&ms according to the mars candy company can be found in the table below. in addition, the table contains the number of m&ms of each color that were found in a case of candy. at the 3% level, do the observed frequencies support the claim of m&m?
m&m observed counts and expected proportions
hypotheses
h₀ :the distribution of color of m&ms is the same as the stated distribution.
hₐ :the distribution of color of m&ms differs from the stated distribution.
expected frequencies
find the expected frequencies (round values to 2 decimal places):
test statistic
the formula set up of the first and last term of the test statistic are as follows:
round initial values to 2 decimal places:
χ² = σ (o - e)² / e

Explanation:

Step1: Calculate the first term of the test statistic

For blue M&M's:
Observed \(O = 488\), Expected \(E=629.28\)
\(\frac{(O - E)^{2}}{E}=\frac{(488 - 629.28)^{2}}{629.28}=\frac{(- 141.28)^{2}}{629.28}=\frac{19960.44}{629.28}\approx31.72\)

Step2: Calculate the last term of the test statistic

For yellow M&M's:
Observed \(O = 365\), Expected \(E = 340.86\)
\(\frac{(O - E)^{2}}{E}=\frac{(365-340.86)^{2}}{340.86}=\frac{(24.14)^{2}}{340.86}=\frac{582.74}{340.86}\approx1.71\)

Answer:

The first - term (for blue) is approximately \(31.72\) and the last - term (for yellow) is approximately \(1.71\)