Question

1. (8 pts total) Assume that a single fair die is tossed 100 times. Let X denote the number obtained in a given toss (so X is 1, 2, 3, 4, 5, or 6). Suppose that x = 2.83 for these 100 tosses. It can be shown that µ = 3.5 and σ =35/12 = 2.91666 . . . (a) (7 pts) Find a 95% confidence interval for µ, based on the given value of x. (b)(1 pt) Did the interval you constructed trap the true mean µ? (should get 2.83±0.572 for part a)

Answer 1

(A) z critical for 95% interval is z = 1.96 (using z table)

population standard deviation

sample mean

sample size n = 100

confidence interval =

(B) Confidence interval obtained in first part is

CI = (2.258, 3.402)

Population mean 3.5 is not included in the confidence interval as the upper limit of confidence interval is below the population mean.