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for the uniform discrete distribution. 1. Use R to generate 600 samples, each containing 40 measurements from this population (with replacement). 2. Calculate the sample mean for each of the 600 samples. 3. Construct a relative frequency histogram for the 600 values of . 4. How does the mean of the sample means compare with the mean of the original distribution? 5. i) Divide the standard deviation of the original distribution by √√40. ii) How does this result compare with the standard deviation of the sample means distribution? 6. Explain how the graph of the distribution of sample means suggests that the distribution may be approximately normal. 7. For each sample size n = 2, 5, 10, 50, 100, construct a relative frequency histogram of the 600 values of . 8. What changes occur in the histograms as the value of n increases? What similarities exist? 9. i) Repeat questions 7 and 8 with n = 150, 200, 250, 300. ii) Explain how the results above illustrate the Central Limit Theorem. 10. a) Repeat questions 7 and 8 for the 600 values of the sample variance s². b) Repeat questions 7 and 8 for the 600 values of the sample median M. c) Does it appear that and Mare unbiased estimators of the population mean? d) Does it appear that s is a biased estimator of the population standard deviation σ? Reflection. - Write a paragraph about the purpose of the study, the problem analysed, and your findings.

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