- 3 25 Points Consider The Following Data 4 9 290 11 843 9 811 9 160 9 125 9 352 9 024 10 710 9 704 9 417 10 346 12 68 1 (156.27 KiB) Viewed 42 times
3. (25 Points) Consider the following data 4- 9.290 11.843 9.811 9.160 9.125 9.352 9.024 10.710 9.704 9.417 10.346 12.683 9.825 10.135 10.079 8.841 10.536 10.165 8.910 10.705 (a) Generate 95% confidence intervals for i. The mean of the distribution based on the t-test. ii. The mean, the median and the standard deviation using the bootstrap. Include your R code in your report. (b) In preparation for this question test if these data have been generated from a Normal(μ = 10, o² = 1) using the Kolmogorov-Smirnov test (use the ks. test command in R; see the help page for instructions on how to use it). State the null hypothesis and if you reject it or not. Use a = 0.05 for your test. In reality, the data is not normally distributed. It was generated using the following R code: a < 2; b < 1/sqrt(a) x < 10 -a*b+rgamma (20, shape = a, scale = b) Use Monte Carlo integration to compute the power of the K-S test for rejecting the hypothesis stating that the distribution of data with these characteristics is Normal( = 10, o² = 1). Use a = 0.05. Explain your procedure and include your R code. Use these results to explain your original result. 2