Question

part 3 please

In this project, you will collect a sample of plain M&M's, summarize your sample data and compare it to the MARS Company's claims. See below for the distribution claimed by the MARS Company Claimed by MARS Company PLAIN M&M'S Color Distribution in One Package Blue 24.0% Brown 13.0% Green 16.0% Orange 20.0% Red 13.0% Yellow 14.0% PARTI - Summarizing and Graphing Data 1. For your sample data, organize the information in a distribution table categorized by color. Your table should include columns for frequency, proportion (as a fraction and a decimal), and percentage of each color. Be sure to appropriately label your table and total each column. 2. Create TWO pie charts - one for your sample data and one for the company's claims. Create ONE split bar chart that includes both your sample data and the company's claims. 3. Compare your sample data to the company's claims. Did your sample data have a similar distribution of colors as claimed by the company? Are you surprised by this? Explain. Be sure to comment on any similarities and differences for each color. PART II - Statistical Analysis 1. Based on your sample data, construct 90% confidence intervals to estimate the proportion (or percentage) of each color. Write out an interpretation for each confidence interval. Based on your confidence interval limits for each color, would you disagree with any of the company's claims? Explain your reasoning. 2. Using your sample data, conduct a hypothesis test for each color to determine if the proportion (or percentage) of candies is different than what is claimed by the company. Use a 0.05 level of significance. Be sure to state your hypotheses, the test statistic and the p-value for each test. What is the conclusion of each hypothesis test? Be sure to explain the results of each test in context. 3. One of the issues with a study such as this one is the small size of the samples. If you wanted to estimate the true percentage of each color of candy to within 1.5%, how many of each color should you sample? Use the company's claimed percentage for each color as an estimate of the target proportion, and assume you want to be 99% confident in your results.

Answer 1

3. For Blue:

Sample size = 5378.690 = 5379

For Brown:

Sample size = 3335.141 = 3336

For Green:

Sample size =3963.245 = 3964

For Orange:

Sample size =4718.149 = 4719

For Red:

Sample size = 3335.141 = 3336

For Yellow:

Sample size = 3550.407 = 3551

All answers are calculated in Excel.

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