Question

You will be doing Chi-square goodness-of-fit testing on the M&M’s in a bag. Steps: 1. Count the number of M&M’s in your bag by color. Red: 12 brown 8 Orange 13 yellow 15 green 9 blue 11 2. Now follow the steps for Hypothesis testing: i. State Null and Alternate hypothesis. Your hypothesis must be based on the assumption that the M&M’s in your bag are expected to follow the following pattern: 24% cyan blue, 20% orange, 16% green, 14% bright yellow, 13% red, 13% brown. ii. Select a level of significance iii. Formulate a decision rule. Calculate critical value iv. Conduct a sample, calculate test statistic and make a statistical decision. v. Make a Business Decision. 3. . I want you to turn-in a document that addresses each of the above steps in the hypothesis testing.

Answer 1

1)Observed frequency

M&M bag	Red	Brown	Orange	Yellow	Green	Blue	Total
frequency	12	8	13	15	9	11	68

2)

i)The null and alternative hypothesis are,

  

ii)Level of significance = 0.05 (say)

iii) Critical value

  

Decision rule,

Reject H0 if  

iv)

M&M bag	Red	Brown	Orange	Yellow	Green	Blue	Total
Observed	12	8	13	15	9	11	68
Expected	8.84	8.84	13.6	9.52	10.88	16.32	68
(O-E)2 / E	1.130	0.080	0.026	3.154	0.325	1.734	6.449

The test statistic is given by,

At level = 0.05, We failed to reject the null hypothesis.

v)

Decision;

The percentage of M&M in our bag should be 24% blue, 20% orange, 16% green, 14% yellow, 13% red, 13% brown.

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