Question

Milk Chocolate M&M’s come in 6 colors; blue, orange, green, yellow, red, and brown.

Choose the color of M&M’s you will be working with for this project

Color: GREEN

Using the collected data below from a single fun-sized bag, provide the frequency and proportion of M&M’s in your color of choice.

Red	Orange	Yellow	Green	Blue	Brown
2	1	2	3	5	1

Number of M&M's in your color:

Total number of M&M's:

Proportion of M&M's in your color:

Construct a 95% confidence interval for the proportion of M&M’s one can expect to find in the color of your choice.

Check the requirements for constructing a confidence interval for the proportion are satisfied. Show your work. (See the note in the blue box on page 426)

The conditions might not be satisfied, depending on how many candies were in your bag. If the conditions are not met, what could you do? (Note—you don’t have to redo the experiment to meet the conditions, just say what you would do.)

Answer 1

Milk Chocolate M&M’s come in 6 colors; blue, orange, green, yellow, red, and brown.

Choose the color of M&M’s you will be working with for this project

Color: GREEN

Using the collected data below from a single fun-sized bag, provide the frequency and proportion of M&M’s in your color of choice.

Red	Orange	Yellow	Green	Blue	Brown
2	1	2	3	5	1

Number of M&M's in your color:3

Total number of M&M's: 14

Proportion of M&M's in your color:3/14 =0.2143

Construct a 95% confidence interval for the proportion of M&M’s one can expect to find in the color of your choice.

Confidence Interval Estimate for the Proportion
Data
Sample Size	14
Number of Successes	3
Confidence Level	95%
Intermediate Calculations
Sample Proportion	0.214285714
Z Value	1.96
Standard Error of the Proportion	0.1097
Interval Half Width	0.2149
Confidence Interval
Interval Lower Limit	-0.0007
Interval Upper Limit	0.4292

95% CI = ( -0.0007, 0.4292)

Check the requirements for constructing a confidence interval for the proportion are satisfied. Show your work. (See the note in the blue box on page 426)

np = 14*0.2143 =3

n*(1-p) = 14*(1-0.2143 ) =10.9998

np is less than 5. Normal approximation is not appropriate.

The conditions might not be satisfied, depending on how many candies were in your bag. If the conditions are not met, what could you do? (Note—you don’t have to redo the experiment to meet the conditions, just say what you would do.)

We can use exact Binomial probabilities.