3. (2pts) Use the StatCrunch file MAT 133 (FA21) Random Confidence Levels to generate a random confidence level for #4 below. (Use Data - Sample, then choose the "Confidence Levels" column and a sample size of 1 then click Compute!) State the confidence level here:4. (6pts) Regardless of whether or not the requirements were met, construct a confidence interval for the proportion of M&M's that are your color from #1 using the confidence level generated in #3. (Show formula, substitution, and result - Note: if typing, use an equation editor) Formula: Substitution: 5. (4,013) Willy Wonka claims that the proportion of candies of your chosen color is more than 1/6\" of any bag. Does your confidence interval support or contradict his claim? (Highlight one) Explain using the interval. Support Contradict Explanation: 6. (6pts) Using the proportion of your color of M&M's as a prior estimate and your confidence level found in #3, calculate the minimum bag size (as in number of candles) required to ensure that the proportion of your color of M&M's is within 1% ofthe true population proportion for that color. (Show formula, substitution, and result - Note: If typing, use an eguation editor) Substitution: a PDF file. Part 1: Confidence Interval with M&M's - 26 points 1. (2pts) Which M & M color had the highest count in your sample? (If there's a tie, just choose one). Fill out this table for that color. (Give 3 decimal places for p) 8 Blue (Color) M&M's in Your Bag X = 8 n = 22 P =0.364 2. (6pts) Verify whether all the requirements for constructing a confidence interval for the proportion of this color of M&M's are satisfied. Show work and/or explain each one. (Note: If typing, use an equation editor) Number of Items of Interest, x = 8 Sample Size, n = 22 Sample Proportion, $ =x = 0.3636 Level of Significance, a = 0.05 Z-value = Za/2 = 1.960 excel formula =NORMSINV(a/2)] Standard Error, SE = V[p(1-6)] = 0.1026 margin of error, E = Z*SE = 1.96*0.1026= 0.2010 Confidence Interval is Interval Lower Limit = 8 - E = 0.3636-0.201= 0.1626 Interval Upper Limit = p + E = 0.3636+0.201= 0.5646 95% Confidence interval is ( 0.163