E = t2/2 NAMES Colors of M&Ms Consider the population of milk chocolate plain M&Ms candies (all plain M&Ms produced by Mars Corp.). Suppose you want to learn the distribution of colors of these candies. 1. BEFORE you count your M&Ms, calculate the minimum sample size you would need in order to estimate the population proportion of a particular color M&Ms within 1% (E-0.01), at a 95% level of confidence. (Hint: since you do not have an initial estimate for p, what number will you use?) Now, choose any M&M color. Count your M&Ms and fill in the chart below. Chosen Color: Red Number of that color Total M&Ms in bag Proportion of your color in bag: Number Notation 11 X 83 n 2. Is the proportion of your color M&Ms calculated above a parameter or a statistic? Is the proportion of your color of all M&Ms produced by the Mars Corp. a parameter or a statistic? What symbol represents it? 3. Since we do not know the true population proportion of your chosen color, we will need to use a confidence interval to estimate it. Use the data from your bag of candy to construct a 95% confidence interval for the true population proportion of your color M&Ms. Interpret the confidence interval you found in a sentence: 4. Earlier, you calculated a point estimate for p. Use that point estimate to recalculate how large a sample of M&Ms would you need to estimate the population proportion of your color M&Ms within 1 percent (E= 0.01) at a 95% level of confidence: 5. Compare the answer from Question 4 to the answer from Question 1. How did the minimum sample size change?