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# HW9 - Stat 4714 HW 9 Due Friday October 29 at 1:15pm 1 The...

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Stat 4714 HW 9 - Due Friday October 29 at 1:15pm 1. The goal of this problem is to have you simulate data from a non-normal distribution and construct a distribution for the sample mean. [TURN IN LIST OF MEANS AND HISTOGRAMS. DO NOT INCLUDE THE SIMULATED DATA] a. Using JMP, simulate 20 random samples of data of size 10 from an exponential distribution with mean 1.5. b. List the 20 sample means from your data. c. Create a histogram of the means. d. Does this distribution of sample means look like it follows a normal distribution? e. Increase the sample size of the 20 samples to 45. Repeat steps b & c using the newly simulated data. Does this distribution of sample means look like it follows a normal distribution? 2. When constructing a confidence interval for a population mean with a known population variance, a. what value of z would we use for a 93% confidence interval? b. what value of z would we use for a 80% confidence interval? c. what value of z would we use for a 85% confidence interval? 3. Find the method of moments estimator for p for the geometric distribution. 4. Find the maximum likelihood estimator for p for the geometric distribution. Note: You may need to use some of the rules for products and logs on the next page. 5. From a random sample of 35 observations, we have obtained a sample mean of 18.5. The population standard deviation is 10. We wish to construct a confidence interval for the mean, but we think our margin of error is too large.

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