Question

This week we will look at the test for goodness of fit. In order to complete this discussion board, you will need a small bag of plain m&m’s.   M&m’s have six colors, listed below. The Mars Candy Company has published the percentage of each color that we should see in any given bag of m&m’s. We are going to determine if our purchases m&m’s are significantly different from what we should expect.

Our Null Hypothesis is that our percentages will match those provided by the company.

Our Alternate Hypothesis is that our percentages will not match those provided by the company.

Step 2:

Average your information with the information from two other students (three students total). This information is the OBSERVED data.

Observed data to be averaged:

• Color	Blue	Orange	Green	Yellow	Red	Brown	Total
  Number of M&M's	5	16	19	5	4	6	55
  Percent of Total	9%	29%	35%	9%	7%	11%	100%

  Color	Blue	Orange	Green	Yellow	Red	Brown	Total
  # of M&Ms	24	22	27	13	7	10	103
  % of Total	23%	21%	26%	13%	7%	10%	100%

• Color	Blue	Orange	Green	Yellow	Red	Brown	Total
  Number of m&m’s	13	5	3	10	9	5	45
  Percent of Total	29%	12%	7%	21%	20%	12%	100%

The EXPECTED data is published by the Mars Candy Company and is listed below:

Color	Blue	Orange	Green	Yellow	Red	Brown	Total
Percent of Total	24%	20%	16%	14%	13%	13%	100%

Calculate the chi-square statistic using the formula on page 656 in your book, or use your calculator.

Then using a 0.05 level of significance and 5 degrees of freedom (because there are 6 colors), determine if we reject our Null Hypothesis or not.  

Answer 1

Result:

Average your information with the information from two other students (three students total). This information is the OBSERVED data.

Observed data to be averaged:

·

Color	Blue	Orange	Green	Yellow	Red	Brown	Total
Number of M&M's	5	16	19	5	4	6	55
Percent of Total	9%	29%	35%	9%	7%	11%	100%

Color	Blue	Orange	Green	Yellow	Red	Brown	Total
# of M&Ms	24	22	27	13	7	10	103
% of Total	23%	21%	26%	13%	7%	10%	100%

·

Color	Blue	Orange	Green	Yellow	Red	Brown	Total
Number of m&m’s	13	5	3	10	9	5	45
Percent of Total	29%	12%	7%	21%	20%	12%	100%

The EXPECTED data is published by the Mars Candy Company and is listed below:

Color	Blue	Orange	Green	Yellow	Red	Brown	Total
Percent of Total	24%	20%	16%	14%	13%	13%	100%

Calculate the chi-square statistic using the formula on page 656 in your book, or use your calculator.

Then using a 0.05 level of significance and 5 degrees of freedom (because there are 6 colors), determine if we reject our Null Hypothesis or not.  

				Total observed	expected%	expected
Blue	5	24	13	42	(42/100)*203=24	48.72
Orange	16	22	5	43	(43/100)*203=20	40.6
Green	19	27	3	49	(49/100)*203=16	32.48
Yellow	5	13	10	28	(28/100)*203=14	28.42
Red	4	7	9	20	(20/100)*203=13	26.39
Brown	6	10	5	21	(21/100)*203=13	26.39
Total	55	103	45	203		203

Goodness of Fit Test
	observed	expected	O - E	(O - E)² / E
	42	48.720	-6.720	0.927
	43	40.600	2.400	0.142
	49	32.480	16.520	8.402
	28	28.420	-0.420	0.006
	20	26.390	-6.390	1.547
	21	26.390	-5.390	1.101
Total	203	203.000	0.000	12.126
	12.126	chi-square
	5	df

Critical chi square value with 5 df at 0.05 level =11.07

Calculated chi square 12.126 > critical chi square value 11.07.

Ho is rejected.

There is enough evidence to conclude that our percentages will not match those provided by the company.