1. Consider the population of ALL the M&M candies manufactured by the Mars Company. Suppose that you want to learn about the distribution of colors of these candies but you can only afford to take a sample of 50 candies. Record the number of each color of M&Ms: Red: 9 Orange:15 Green:10 Yellow:5 Blue:4 Brown:7 For now, we will only focus on the orange candies. The number of M&Ms you have is the sample size, n. The number of orange candies in your sample is x. Record the number of orange M&Ms in your sample. n = 50 x = __15_____ a. Is the proportion of orange M&Ms in your sample a parameter or a statistic? What symbol represents it? b. Do you know the value of the proportion of orange M&Ms in your sample? If so, calculate it. c. Is the proportion of all orange M&Ms manufactured by Mars a parameter or a statistic? What symbol represents it? d. Do you know the value of the proportion of all orange M&Ms manufactured by Mars? If so, calculate it. e. Clearly the students in this class will get many different values for their sample proportion of orange M&Ms. What statistical term refers to this phenomenon? (Hint: two words, the first one starts with "s" and the second one starts with "v"). f. Check the conditions for calculating the confidence interval estimating the proportion of orange M&Ms manufactured by Mars. Are they satisfied? (Even if they are not, keep working on the problems below). = (1 ) = g. Calculate a 95% confidence interval using the sample values to estimate the proportion of ALL orangeM&Ms. h. Write the correct in context interpretation of this interval in words (refer back to your notes). i. What is the margin of error of your confidence interval? j. How many M&Ms should we have in our sample if we want the margin of error to be half of what you got in part i? k. What percent of all of the calculated 95% confidence intervals should contain the population parameter? l. Would the 90% confidence interval be wider or narrower? m. If we had 100 M&Ms in our sample instead of 50, would the 95% confidence interval wider or narrower? n. According to their website, the proportion of orange M&Ms produced at the Cleveland factory is 20.5%.Is this value in your confidence interval? o. We want to test the claim that the proportion of orange M&Ms is 20.5%. Write the null and alternativehypothesis for the test. Use a two-sided test. p. Are the conditions for the hypothesis test satisfied? 3= (1 3) = q. Find the test statistic. Draw the sampling distribution and shade the appropriate area(s). r. Find the -value using your z-table. s. If the true proportion of orange M&Ms is truly 20.5% but we reject this hypothesis, then what type oferror did we make?