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3. Let our population be {2, 5, 6}. We will take samples of size n=2 from this population. Take all possible samples of size 2, with replacement. Check if sample median is an unbiased estimator of population median. (i.e. check if mean of all sample medians targets population median)

3. Let our population be {2, 5, 6}. We will take samples of size n=2 from this population. Take all possible samples of size 2, with replacement. Check if sample median is an unbiased estimator of population median. (i.e. check if mean of all sample medians targets population median)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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### Statistical Exercises #### Problem 3: - **Task**: Consider a population {2, 5, 6}. We will take samples of size \( n = 2 \) from this population. Take all possible samples of size 2, with replacement. Determine if the sample median is an unbiased estimator of the population median (i.e., check if the mean of all sample medians equals the population median). #### Problem 4: - **Scenario**: The population mean of the distribution of heights of elderly English women is 160 cm with a standard deviation of 6 cm. The distribution of heights is normally distributed. We will take simple random samples of 16 women from this population. - **Questions**: - a) Can we assume that the distribution of sample means \( \bar{x} \) is normal? Why or why not? Explain. - b) If possible, find the probability that in a random sample of 16 elderly English women, the mean height is less than 156 cm. #### Problem 5: - **Scenario**: The population mean height for 3-year-old boys is 38 inches, and the population standard deviation is 3 inches. Assume that heights are normally distributed in the population. - **Questions**: - a) Find the probability that a randomly chosen 3-year-old boy is shorter than 36 inches. - b) Find the probability that in a randomly chosen sample of 15 3-year-old boys, the mean height is less than 36 inches. We want \( P(<36) \). #### Problem 6: - **Scenario**: Women have head circumferences that are normally distributed with a mean of 22.65 inches and a standard deviation of 0.8 inches.
Transcribed Image Text:### Statistical Exercises #### Problem 3: - **Task**: Consider a population {2, 5, 6}. We will take samples of size \( n = 2 \) from this population. Take all possible samples of size 2, with replacement. Determine if the sample median is an unbiased estimator of the population median (i.e., check if the mean of all sample medians equals the population median). #### Problem 4: - **Scenario**: The population mean of the distribution of heights of elderly English women is 160 cm with a standard deviation of 6 cm. The distribution of heights is normally distributed. We will take simple random samples of 16 women from this population. - **Questions**: - a) Can we assume that the distribution of sample means \( \bar{x} \) is normal? Why or why not? Explain. - b) If possible, find the probability that in a random sample of 16 elderly English women, the mean height is less than 156 cm. #### Problem 5: - **Scenario**: The population mean height for 3-year-old boys is 38 inches, and the population standard deviation is 3 inches. Assume that heights are normally distributed in the population. - **Questions**: - a) Find the probability that a randomly chosen 3-year-old boy is shorter than 36 inches. - b) Find the probability that in a randomly chosen sample of 15 3-year-old boys, the mean height is less than 36 inches. We want \( P(<36) \). #### Problem 6: - **Scenario**: Women have head circumferences that are normally distributed with a mean of 22.65 inches and a standard deviation of 0.8 inches.
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