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2. [5 marks] We again wish to construct 100 confidence intervals with confidence level 95% from a Binomial distribution with n =20 and p = 0.1. Step 1: Start a new worksheet. Step 2: Generate 100 samples of size 200 from a Binomial distribution with n =20 and p = 0.1. Store the results in columns C5 - C204. You can do this using the following commands: Random 100 c5-c204; Binomial 20 .1. Each of the first 100 rows in your spreadsheet now contains a random sample of 200 observations from a Binomial distribution with n =20 and p = 0.1. Step 3: Label column C4 as "xbar" and use it to store the sample means of each of the 100 samples. You can compute these by using the following commands: rmean c5-c204, c4 Step 4: Label column C2 as "lower bound" and C3 as "upper bound". These columns will store the lower and upper bounds for the confidence intervals that we compute based on each of the 100 samples. To compute the lower and upper bounds of each interval, use the commands: let c2 = c4 - 1.96*sqrt(0.1*0.9/10) let c3 = c4 + 1.96*sqrt(0.1*0.9/10) Step 5: We wish to determine how many of your 100 confidence intervals do contain the true mean u - 2. To do this, enter the following command let cl = (c2 2) If a confidence interval contains the mean value u = 2, the corresponding entry in column Cl will now contain a 1; otherwise, it will contain a 0. To determine how many of the intervals did contain = 2, use the following command: tally cl Questions: A. [2] What percentage of the intervals actually did contain the true mean u = np = 2? B. [3] Based on the interpretation on a 95% confidence interval, is this the number expected? Explain