Question

Based on classical probabilities for a “normal flavor” bag of Skittles, each of the five flavors (Yellow, Green, Red, Purple, and Orange) should have a 1/5 or 20% proportion. Skittles reports that deviations can occur, and consumers should expect anywhere between 15 to 23 percent composition of any color when they open their bag. You want to test this proportion based on a confidence interval thus you have sampled 27 bags with various counts in each bag and reported on the Excel spreadsheet.

Create an 88% confidence interval for each color. Break down your interval by first reporting your standard error. Then, after reporting your interval, explain the meaning of your interval values and your thoughts on what the company has stated for the true population proportions. One thing to be sure and note if any colors fell outside the true interval for the population.

N	Yellow	Green	Red	Purple	Orange
106	21	29	18	14	24
99	18	20	21	17	23
96	22	18	18	22	16
96	9	17	24	15	31
99	20	16	19	20	24
96	22	13	12	18	31
97	20	17	22	23	15
110	26	25	20	17	22
106	15	29	13	24	25
97	16	17	23	19	22
98	24	20	23	8	23
108	18	19	32	18	21
96	18	17	22	20	19
96	10	27	25	21	13
97	18	21	29	15	14
95	14	15	23	18	25
110	29	25	25	17	14
96	17	19	20	21	19
97	18	25	19	14	21
95	24	12	20	19	20
97	19	23	19	16	20
108	13	23	23	22	27
97	19	21	19	26	12
107	27	24	20	17	19
111	29	24	17	22	19
110	20	20	26	19	25
110	17	25	22	22	24

Answer 1

1. Put the data in excel as shown below.

2. Calculate the proportion of each colour gem in a pack

3. Next we use these proportion to find the 88% confidence interval as shown below.

Each of the interval indicates that we are 88% confident that the proportion of a particular colour will lie in the given interval.

We see that for all the colours the proportion is beyond the true proportion.