Question

What are the proportions for the colors of M&M candy colors? You will need one Medium (approximately 12 ounce) bags of M&M’s. You may choose from any of the following varieties:

• • Peanut
• • Dark
• • Coconut
• • Almond
• • Crispy
• • Peanut Butter
• • Pretzel

Answer each of the questions below for your bags of candy in your project. Your final project should be in report form which includes the answers to the questions. The report should be typed. You may hand write neatly the mathematics symbols and your work. If you have any questions, you should contact your teacher.

1. A) Basics Information:

1. 1) Identify the colors of M&M’s that are in one of your packages. Be sure to indicate the variety of M&M and name the colors.
2. 2) Before you begin the data collection, state the percentages of colors that you think are in the bag. (2 points)
3. 3) Make a frequency distribution of the counts of the colors in your first bag and give the relative frequency for each color. (3 points)

Color	Frequency	Relative Frequency
Blue
Brown
Green
Red
Orange
Yellow

4) The “color” of M&M is what type of data (two answers)? (1 point)

5) Graph the data by using an appropriate chart. (May use excel and paste the graph in the report). State why you chose you type of graph. (5 points)

B) Proportion test (you may use <, >, or ≠ for H₂):

Now, choose color. Just test one of the colors. Use the official proportion from M&M’s for p and compare to your proportion,. Use 5% for level of significance

1. 1) State the null and alternate hypotheses. (4 points)
2. 2) Find test stat and the P-value. (8 points)
3. 3) Sketch the sampling distribution and show the area corresponding to the P-value.(4 pts
4. 4) Will you reject or fail to reject the null hypotheses? State your conclusion in the context of the data. (9 points)

C) Good ness of fit

1) Do you think that the data you have gathered agrees with the company’s claims? (2 points)

2) Identify a procedure that you could use to check the goodness of fit for your data on one of the variety of M & M’s. (1 point)

3) Identify the H_o and H₁ you would use to verify the company’s claim. (4 points)

4) Display in a matrix the observed and expected cell values and perform a Chi-Square analysis for the one of M & M’s variety (10 points)

Color	Observed	Expected	(O – E)²/E
Blue
Brown
Green
Red
Orange
Yellow

5) Write a word conclusion to the hypothesis test you have performed using the 1% level of significance. (Show all steps in your hypothesis test) (9 points)

D) Test for Independence

Now consider the type of M&M and the color. Use the one sample that you counted and one sample given to you (below) to test the hypothesis that the type of M&M is independent of the colors as listed.

1) Fill in your data in the chart below (3 points)

Actual	Color	Blue	Brown	Green	Orange	Red	Yellow	Total
Plain	Frequency	126	99	35	86	67	83	496
Your M&M’s	Frequency
	Total

2) Filled in the expected amounts (6 points)

E = (Row total)(Column Total)/ Sample Size

Expected	Color	Blue	Brown	Green	Orange	Red	Yellow	Total
Plain
Your M&M’s
	Total

3) Identify the H_o and H₁ you would use to verify the type of M&M is independent of the colors as listed.   

4) Perform a Chi-Square analysis for the two of M & M’s variety

Chi-Square (O-E)2/E	Color	Blue	Brown	Green	Orange	Red	Yellow	Total
Plain
Your M&M’s
	Total

5) Write a word conclusion to the hypothesis test you have performed using the 5% level of significance.   

Answer 1

(A).

(1). I have the M7M's peanut chocolate candy and the color of my M&M's are

1. Brown
2. Red
3. Yellow
4. Green
5. Blue
6. Orange

(2). I think there should be equal percentage of color of M&M's. Since, the M&M's contain 6 colors so I think the percentage of each color should be (1/6)*100 = 16.67%

(3). frequency and relative frequency table is given below:

(4). The color of M&M's is a qualitative data because we can not measure measure on any numeric scale.

(5). Here we use bar chart to represent our data because we want to compare the frequencies of different color of M&M's. And also bar graph gives quick information regarding the quantity displayed of particular category and their relative proportion.

To construct bar graph in excel, do the following given steps:

1. Firstly enter the data into excel
2. Then select the data,that is column named color and frequency
3. Then go to insert option in the toolbar.
4. Under the insert, there is chart section, then click on bar graph and OK.