6.5.4 Suppose the number of calls arriving at an answering service during a given hour of the day is Poisson(2), where 1 e (0, co) is unknown. The number of calls actually received during this hour was recorded for 20 days and the following data were obtained. 9 10 8 12 11 12 5 13 9 9 7 5 16 13 9 5 13 8 9 10 Construct an approximate 0.95-confidence interval for 1. Assess the hypothesis that this is a sample from a Poisson(11) distribution. If you are going to decide that the hypothesis is false when the P-value is less than 0.05, then compute an approximate power for this procedure when 1 = 10.5. Chapter Exercise {3.5.4. Construct and calculate .a TWald interval. Use that interval to assess the hypothesis and omit the power calculation; Add the following. {b} lConstruct and calculate an approximate level if = [LEE condence interval based on the 3; 1 Ellie's: {c} Carr}.r out a simulation to determine which interval has better coverage properties. {Gen erate N E 101000 Poissonlzll. = 11} samples of size n = 21} and compute both types of intervals for each sample. \"coverage\" = \"interval contains the true value of A\" ] asymptotic pivot {which gives the score interval}