chapter 1

Chapter 5: Joint Probability Distributions and Random Samples43. The statistic of interest is the fourth spread, or the difference between the medians of theupper and lower halves of the data. The population distribution is uniform with A = 8 and B= 10. Use a computer to generate samples of sizes n = 5, 10, 20, and 30 from a uniformdistribution with A = 8 and B = 10. Keep the number of replications the same (say 500, forexample). For each sample, compute the upper and lower fourth, then compute thedifference. Plot the sampling distributions on separate histograms for n = 5, 10, 20, and 30.44. Use a computer to generate samples of sizes n = 5, 10, 20, and 30 from a Weibull distributionwith parameters as given, keeping the number of replications the same, as in problem 43above. For each sample, calculate the mean. Below is a histogram, and a normal probabilityplot for the sampling distribution of x for n = 5, both generated by Minitab. This samplingdistribution appears to be normal, so since larger sample sizes will produce distributions thatare closer to normal, the others will also appear normal.45. Using Minitab to generate the necessary sampling distribution, we can see that as n increases,the distribution slowly moves toward normality. However, even the sampling distribution forn = 50 is not yet approximately normal.n = 10Normal Probability Plot90Frequency807060504030201000 10 20 30 40 50 60 70 80 90Probability.999.99.95.80.50.20.05.01.001515253545n=1055657585Anderson-D arling N ormality Tes tA-Squared: 7.406P-Value: 0.000n = 50Normal Probability PlotFrequency7 06 05 04 03 02 01 0Probability.999.99.95.80.50.20.05.01.001020304050601 525354 55565An de r so n- Da rl ing No r mali ty Te s tA- Sq ua re d : 4. 42 8P-Va lue : 0 .0 00190