Now that we have gathered some information about M&M’s, we want to look at our data more closely and make some decisions about the distribution of the colors in the M&M bags.For this project, you will be examining the distribution of a certain color (your pick from the first project) in your original bag of M&M’s, plus an additional bag of another type of M&M’s.Do they match the following amounts?
- 24% Blue
- 20% Orange
- 16% Green
- 14% Yellow
- 13% Red
- 13% Brown
This project will be a formal paper. This means that you will create a new Word document for this project. It is important to be able to communicate clearly and concisely in the business world. You should use full sentences.Correct spelling and grammar are important.Make sure your paper is well organized and that you cover all the necessary information.The paper should have the following:
- Typed, 12 point Ariel font
- Double Spaced
- Introduction
- A full discussion of Parts A, B, C, and D including any work needed to carry out the calculations and hypothesis tests.
- Conclusion
You will save your paper as a Word document and upload it to Blackboard in the Project Part 2 drop box. Feel free to contact me with any questions!
Directions
Part A1
- Based on your original M&M’s data and the color you chose, you will calculate a 50% confidence interval, a 75% confidence interval and a 95% confidence interval.You will input your intervals in the Excel Sheet “Confidence Intervals for M&M project” in the Project Part 2 folder.You only need to submit for your chosen color.There is a separate drop box for the return of the Excel spreadsheet.Failure to submit the information in time will lead to a 5 point deduction on the Part 2 Project grade.
- You will also include the calculations and information about the confidence intervals in the project paper.
- Is the population proportion for your color in your three confidence intervals? (For example, if you choose blue, is .24 in the intervals that you calculated?)
Part A2
Part B1
- Based on your original M&M’s data and the color you chose; you will do hypothesis testing based on the information given above.In order to set up your alternative hypothesis, you will compare your percent of your color to the color percentage at the beginning of the directions.
- If your percent is lower, then you are asking “Do you have good evidence that the percent of <color> is lower than advertised?
- If your percent is higher, then you are asking “Do you have good evidence that the percent of <color> is higher than advertised?
- Based on the results of your hypothesis test, what does this say for the supposed percent of M&M’s production of your chosen color of M&Ms?You will test at the 5% level of significance.
- Repeat the hypothesis test for the overall relative frequency /percentage of your color from the class data.In order to set up your alternative hypothesis, you will compare your percent of your color to the color percentage at the beginning of the directions.
- If your percent is lower, then you are asking “Do you have good evidence that the percent of <color> is lower than advertised?
- If your percent is higher, then you are asking “Do you have good evidence that the percent of <color> is higher than advertised?
- Based on the results of your hypothesis test, what does this say for the supposed percent of M&M’s production based on the class percent of your chosen color of M&Ms?You will test at the 5% level of significance.
- Does the conclusion change from what you concluded in Part B1?
Part B2
Part C
- You will buy a new bag of M&M’s that is different from the plain milk chocolate ones that you previously bought in Part 1 of the project.State the type, and the count of your chosen color and the total number of M&M’s in the new bag.Calculate the relative frequency / percent of the <color> of M&M’s.
- Based on your new M&M’s data and the color you chose; you will do hypothesis testing based on the information given above.In order to set up your alternative hypothesis, you will compare your percent of your color to the color percentage at the beginning of the directions.
- If your percent is lower, then you are asking “Do you have good evidence that the percent of <color> is lower than advertised?
- If your percent is higher, then you are asking “Do you have good evidence that the percent of <color> is higher than advertised?
- Based on the results of your hypothesis test, what does this say for the supposed percent of M&M’s production of your chosen color of M&Ms?You will test at the 5% level of significance.
- Did you get similar results to Part B?Discuss. add a cookie recipe with M&M’s.
Part D
- Shortly after you have submitted your confidence intervals, the compiled spreadsheet of the confidence intervals will be released on Blackboard.Take a look at the results for your chosen color.Please recall that the population parameters for the distribution of M&M’s are given at the beginning of the directions.
- For the 50% confidence interval for your chosen color, how many of the intervals would you expect to the find the population parameter?How many intervals do contain the population parameter?Compare the two numbers.
- For the 75% confidence interval for your chosen color, how many of the intervals would you expect to the find the population parameter?How many intervals do contain the population parameter?Compare the two numbers.
- For the 95% confidence interval for your chosen color, how many of the intervals would you expect to the find the population parameter?How many intervals do contain the population parameter?Compare the two numbers.
- If there are big differences in either 2, 3 or 4, why do you think that is the case?