Part 1) M&M Color Distribution (5 points)

The Mars Company, makers of M&M candy, claims that in every plain M&M bag there is 13 % red pieces, 14% yellow pieces, 16% green pieces, 20% orange pieces, 24% blue pieces, and 13% brown pieces. The company also states that the colors are blended mechanically according to the formula, but occasionally an unusual assortment of colors may appear.

Aisha got a 32 oz bag of M&M and sorted the pieces according to their colors. She recorded the counts below. She wants to see if her bag of M&Ms follows the claimed color distribution of the Mars Company.

Red

Yellow

Green

Orange

Blue

Brown

Total

Observed counts of M&M pieces for each color

130

149

155

210

252

123

1019

Expected number of M&M pieces for each color

1.What type of hypothesis test is required here?State all assumptions required for this test.

Chi Square Test

Assumption:

Observation should be independent.

Each expected frequency must be at least 5

2.Fill in the row of expected values in the table above.Round each value to 1 decimal place.

3.State the null and alternate hypotheses for this test: (use correct symbols and format!)

Null hypothesis

Alternate hypothesis

4.Using = 0.10, run the correct hypothesis test and provide the information below.Give the correct symbols AND numeric value of each of the following (round answers to 3 decimal places).

Test Statistic

Critical value [HINT: this is NOT ]

Degrees of Freedom

p-value

5.State your statistical decision (and justify it!) and interpret your decision within the context of the problem.What is your conclusion?