Question

Use the Excel data file found in the Course Content from Module #1. Be sure to submit your file through the Project #4 drop box for this week.

Masterfoods USA states that their color blends were selected by conducting consumer preference tests, which indicated the assortment of colors that pleased the greatest number of people and created the most attractive overall effect. On average, they claim the following percentages of colors for M&Ms® milk chocolate candies: 24% blue, 20% orange, 16% green, 14% yellow, 13% red and 13% brown.

1. Test their claim that the true proportion of blue M&Ms® candies is 0.24 at the 0.05 significance level.

2.  Test their claim that the true proportion of orange M&Ms® candies is 0.20 at the 0.05 significance level.

3. Test their claim that the true proportion of green M&Ms® candies is 0.16 at the 0.05 significance level.

4. Test their claim that the true proportion of yellow M&Ms® candies is 0.14 at the 0.05 significance level.

5. Test their claim that the true proportion of red M&Ms® candies is 0.13 at the 0.05 significance level.

6. Test their claim that the true proportion of brown M&Ms® candies is 0.13 at the 0.05 significance level.

7. On average, they claim that a 1.69 oz bag will contain more than 54 candies. Test this claim (µ > 54) at the 0.01 significance (σ unknown).

HELP:

As an example, say we had found 732 purple candies out of 3500 total candies. The sample proportion of purple candies is 732/3500 = 0.2091428571.
Now let's say you want to test that the true proportion of purple candies is 21% (0.21).
First define your hypotheses:
H0: p = 0.21 (claim)
H1: p ≠ 0.21

Next we need to calculate the test statistic. For this type of test, it is a z and a two tailed test. You have been asked to test at alpha = 0.05, so we will reject the null if the test statistic, z, is positive and greater than 1.96 OR if the test statistic, z, is negative and smaller than -1.96. (NOTE: This is the same as if the absolute value of the test statistic is greater than 1.96.)

Review: → sample proportion (0.209143)
p → assumed value in null (0.21)
q → 1 - p (0.79)
n → total number of candies (3500)

Because the test statistic is negatiae and is NOT smaller than -1.96, we FAIL TO REJECT. We have insufficient evidence to suggest the true proportion is not 0.21.

You will follow this procedure for EACH color.

Blue	Orange	Green	Yellow	Red	Brown	Total Number of Candies in Bag
6	17	10	8	10	7	58
8	8	11	12	9	10	58
8	13	14	4	12	7	58
7	13	10	7	14	7	58
12	13	4	13	5	10	57
13	8	12	13	1	10	57
8	8	14	7	9	11	57
16	10	10	5	11	4	56
11	11	8	13	6	7	56
10	9	14	10	9	4	56
6	12	13	8	9	8	56
14	10	2	13	7	10	56
11	10	11	12	5	7	56
14	11	8	6	7	10	56
14	8	9	5	5	15	56
11	12	10	12	7	3	55
12	9	12	8	5	9	55
7	12	10	7	10	9	55
8	9	13	11	10	4	55
10	11	9	10	6	9	55
10	10	9	10	7	9	55
9	3	9	13	8	13	55
10	8	13	10	9	5	55
11	6	11	7	8	12	55
12	13	10	11	5	3	54
12	8	5	15	8	6	54
12	8	5	15	8	6	54
14	14	9	4	6	7	54
13	7	12	9	4	9	54
13	10	11	8	5	6	53
7	11	10	9	7	9	53
9	14	8	6	6	10	53
12	10	8	7	9	6	52
10	7	11	7	8	8	51
11	3	12	8	7	10	51
8	10	12	6	7	6	49

Answer 1

Note : Allowed to solve only 4 questions per post.

Step 1 : Finding the proportion of each type of candy. This done in excel and the formulas are shown below

Here we add up the total candy for each type and divide with the grand total.

1. Test their claim that the true proportion of blue M&Ms® candies is 0.24 at the 0.05 significance level.

There is sufficient evidence to claim that the true proportion of blue M&Ms® candies is different 0.24 at the 0.05 significance level.

2. Test their claim that the true proportion of orange M&Ms® candies is 0.20 at the 0.05 significance level.

Conclusion : There is sufficient evidence to claim that the true proportion of orange M&Ms® candies is different from 0.20 at the 0.05 significance level.

3. Test their claim that the true proportion of green M&Ms® candies is 0.16 at the 0.05 significance level.

There is sufficient evidence to claim that the true proportion of green M&Ms® candies is different from 0.16 at the 0.05 significance level.

4. Test their claim that the true proportion of yellow M&Ms® candies is 0.14 at the 0.05 significance level.

There is sufficient evidence to claim that true proportion of yellow M&Ms® candies is different 0.14 at the 0.05 significance level.