Parameter Estimation + Confidence Interval + Margin of Error Means when o is known Problem#2 23. A simple random sample of size n is drawn from a popula- tion that is normally distributed with population standard deviation, o, known to be 13. The sample mean, x, is found to be 108. (a) Compute the 96% confidence interval for if the sample size, n, is 25. (b) Compute the 96% confidence interval for u if the sample size, n, is 10. How does decreasing the sample size affect the margin of error, E? (c) Compute the 88% confidence interval for if the sample size, n, is 25. Compare the results to those obtained in part (a). How does decreasing the level of confidence affect the size of the margin of error, E? (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? Why? (e) If an analysis of the sample data revealed three outliers greater than the mean, how would this affect the confi- dence interval? (a) 102.67 113.33 (b) 99.57 116.42 (c) 103.96 112.04 (d) Yes (e) CI will shift

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Random Variables

A random variable Z is a real valued function of the type Z: S → R on a sample space S. That means the function assigns a real number to every primitive event in the sample space. In other words, a random variable is a function mapping a sample space S to a set of real numbers R.