1. STATISTICS + R CODING
2. Exercise 3 (R) Show all code and relevant output

Exercise 3 (R) Show all code and relevant output Using R, generate a random sample of size n=10 from the following Normal Distribution: N(/ = 100, o? = 25). a) (0.25 pt) Use R to find the sample mean X, and sample variance s'. Show your output. b) (0.5 pt) Assume that the true variance is unknown. Using the sample variance, generate a 95% confidence interval for /. c) (1 pt) Generate 500 independent samples of size n=10 from the same Normal distribution above. Use each of these samples to generate a 95% confidence interval for #. (you will generate 500 different intervals) How many of your confidence intervals captured the true parameter value for ? Show your code and final output (answer) for this step. (You do not need to output all the confidence intervals)d) (0.75 pt) Now assume that the true variance is known, (o' = 25). Repeat part (c), generate 500 new samples and 500 new confidence intervals for /. How many of your confidence intervals captured the true parameter value for /? Show your code and final output for this step. e) (0.5pt) Compare the intervals from part (c) and part (d), which one is larger on average