Use JAGS (or OpenBUGS) to carry out your analysis. Data for both problems are in the accompanying workbook, Data for Chapter 8 Homework.xlsx Problem 8-1. Applying reasonable assumptions for your likelihood and priors, a. Estimate the mean and standard deviation of the data in the Prob 8-1 Data worksheet. b. Predict the next (i.e., 21st) value c. Perform, at a minimum, three diagnostic tests: gelman plot, chain mixing plots (e.g., an xyplot), and density plots Problem 8-2. Perform a Bayesian t-test on means of the two vectors in Prob 8-2 Data worksheet. a. Create a boxplot of the two vectors b. Develop and plot the distribution of the difference between the two vectors c. Whats the probability that one vector is different than the other? d. Whats your inference about the difference between the difference between the two vectors?

#### Data for prob. 8-1

y <- c(46,58,40,47,47,

53,43,48,50,55,

49,50,52,56,49,

54,51,50,52,50)

### Data for Prob. 8-2

#### Load the first variable, y1

# Paint rows 9 through 47; then run. Check to see if you loaded

# the data by running row 48

y1 <- scan()

38.8553906

37.72697879

33.9927533

28.28042042

44.85345117

42.37323534

27.88641307

47.06868786

46.14588539

43.38863826

40.98222931

39.91336814

37.83431795

36.20538628

32.26228853

56.32063644

31.00440411

38.3647674

46.93443409

43.00464714

36.60734971

31.07214685

43.89040099

32.88871042

40.13798746

57.28880461

50.28243855

44.97124922

51.25137263

37.1055347

47.99782492

42.79146886

48.62850745

39.27568216

36.42870611

30.58131302

length(y1)

print(y1)

### Load the second variable, y2

# Paint rows 55 through 97; then run. Check to see if you loaded

# the data by running row 98

y2 <- scan()

47.13782469

37.73630642

30.47735768

44.52019865

24.58812192

36.82541191

44.28001745

24.78833396

34.06576448

30.57757167

31.94306958

36.13935844

35.98491236

40.14024383

39.36550232

34.6459198

40.53653143

30.89848625

55.12277878

48.84548083

33.44247004

53.67390563

19.19676362

58.42801752

38.71277052

38.58246061

27.74643761

36.5683806

29.87023862

39.22827839

45.54786713

32.72168699

46.81731985

45.27289966

44.73590622

48.15835077

23.10200093

54.32440014

38.43423327

48.02179611

length(y2)

print(y2)