Question 2 1. In R, simulate one observed sample of size 100 from N(μ, 4) where μ = 3. We want to test Hoμ = 3 and H₁ μ3. Compute the

observed test statistics for T from the obtained sample, assuming that the population SD o is unknown. Reject the null hypothesis if the absolute value of the observed test statistic is greater than or equal to t(99).025 = 1.984. Which decision do you make? 2. Repeat Step 1 for B = 10000 times. Based on the results, estimate type I probability for the test of rejecting the null if the observed test statistic is greater than or equal to t(99).025 = 1.984. 3. Now, simulate one observed sample of size 100 from N(μ, 4) where μ = 3.5. We still want to test Ho: μ = 3 and H₁ μ3. Compute the observed test statistics for T from the obtained sample, assuming that the population SD o is unknown.. Reject the null hypothesis if the absolute value of the observed test statistic is greater than or equal to t(99).025 = 1.984. Which decision do you make? 4. Repeat Step 3 for B = 10000 times. Based on the results, estimate type Il probability for the test of rejecting the null if the observed test statistic is greater than or equal to t(99).025 = 1.984.