12. In this and the next questions, you will conduct simulation studies in R to explore the concepts we learned for hypothesis testing. For the first simulation study, use the rnorm() function to generate one random sample data (with sample size n = 5) from the distribution N(5, 1), and assign this data to an object called sample1. Then, generate another random sample data (with sample size n =5) from the same distribution, and assign this data to an object called sample2. (a) Write down the five scores in sample1 and the five scores in sample2. Attach the R code for generating the sample data. (b) What are the mean score for sample1 and the mean score for sample2? What is the difference between these two means? (c) What is the population mean difference between the two groups of scores? Is it exactly the same with the sample mean difference? Explain why it is or it isn't the same. (d) Use t.test() function to conduct an independent-samples t-test. Our null hypothesis is Ho: 1-2 = 0. Our alternative hypothesis is Ha: 1 - 20. The code for the t-test is provided below. What is your obtained p-value? Suppose = 0.05. Is your test significant (in other words, were you able to reject the null hypothesis)? t.test(sample1, sample 2, var.equal = T) (e) Post your answer to part (d) on the eClass's discussion board designated for this question. wwwwwww (f) I will eventually tally the results across all students and compute the proportion of students who got significant t-test after all assignments are submitted. Discuss on the eClass discussion board whether this proportion represents type I error rate (i.e., a) or power and explain why you pick your answer. Note that for this part, as long as you participated in the discuss and demonstrated your effort in thinking about the question, you will get the full mark. We will talk about the right answer in the final review session.