Question

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

The color is red and the number of candies is 25/200 total M&Ms

1. Choose your favorite color of M&M’s you will be working with for this project. State the color and give the counts below.

Color of choice:

Number of M&M's in your color:

Total number of M&M's:

Proportion of M&M's in your color:

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

3. Give an interpretation of your interval.

4. Find the margin of error for your interval.

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

6. 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.)

7. Does your interval contain the stated proportion by M&Ms for the color you chose?

8. If you had a larger sample, how would you expect the confidence interval to be affected? Provide justification.

Part 2: Discussion Board Post – Confidence Interval (points on discussion board)

Find a confidence interval from a source or article you’re interested in. Post the confidence interval and an interpretation of the article. You can add substance to your post by including some things you find interesting about the article/source you used.

Please post your source.

Answer 1

1. Color of choice: Red

Number of M&M's in your color:

Total number of M&M's:

Proportion of M&M's in your color:

2. For 95% confidence interval, the critical value of z is z*=1.96. The 95% confidence interval for the proportion of red M&M’s is:

3. We are 95% confident that true proportion of red M&M’s lies between 0.079 and 0.171.

4. The margin of error is:

5. Sample was random and independent.

The conditions are all satisfied.

6. If the conditions are not met, we can increase sample size.

7. Proportion of red candies is 0.20 and this proportion of red candies does not lie between 0.079 and 0.171.

8. If you had a larger sample, the confidence interval would be narrower.