Assume a population of 43, 49, 52, and 59. Assume that samples of size n=2 are randomly selected with replacement from the population. Listed below are the sixteen different samples. Complete parts (a) through (c). 43,43 43,49 43,52 43,59 49,43 49,49 49,52 49,59 52,43 52,49 52,52 52,59 59,43 59,49 59,52 59,59 . Find the median of each of the sixteen samples, then summarize the sampling distribution of the medians in the format of a table representing the probability distribution of the distinct median values. Use ascending order sample medians. Sample Median Probability Sample Median Probability (Type integers or simplified fractions. Use ascending order of the sample medians.) o. Compare the population median to the mean of the sample medians. Choose the correct answer below. O A. The population median is equal to half of the mean of the sample medians. O B. The population median is not equal to the mean of the sample medians (it is also not half or double the mean of the sample medians). OC. The population median is equal to the mean of the sample medians. OD. The population median is equal to double the mean of the sample medians. c. Do the sample medians target the value of the population median? in general, do sample medians make unbiased estimators of population medians? Why or why not? O A. The sample medians target the population median, so sample medians are biased estimators, because the mean of the sample medians equals the population median. O B. The sample medians do not target the population median, so sample medians are biased estimators, because the mean of the sample medians does not equal the population median. OC. The sample medians do not target the population median, so sample medians are unbiased estimators, because the mean of the sample medians does not equal the population median.
Assume a population of 43, 49, 52, and 59. Assume that samples of size n=2 are randomly selected with replacement from the population. Listed below are the sixteen different samples. Complete parts (a) through (c). 43,43 43,49 43,52 43,59 49,43 49,49 49,52 49,59 52,43 52,49 52,52 52,59 59,43 59,49 59,52 59,59 . Find the median of each of the sixteen samples, then summarize the sampling distribution of the medians in the format of a table representing the probability distribution of the distinct median values. Use ascending order sample medians. Sample Median Probability Sample Median Probability (Type integers or simplified fractions. Use ascending order of the sample medians.) o. Compare the population median to the mean of the sample medians. Choose the correct answer below. O A. The population median is equal to half of the mean of the sample medians. O B. The population median is not equal to the mean of the sample medians (it is also not half or double the mean of the sample medians). OC. The population median is equal to the mean of the sample medians. OD. The population median is equal to double the mean of the sample medians. c. Do the sample medians target the value of the population median? in general, do sample medians make unbiased estimators of population medians? Why or why not? O A. The sample medians target the population median, so sample medians are biased estimators, because the mean of the sample medians equals the population median. O B. The sample medians do not target the population median, so sample medians are biased estimators, because the mean of the sample medians does not equal the population median. OC. The sample medians do not target the population median, so sample medians are unbiased estimators, because the mean of the sample medians does not equal the population median.
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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Assume a population of 43, 49, 52, and 59. Assume that samples of size n = 2 are randomly selected with replacement from the population. Listed below are the sixteen different samples. Complete parts (a) through (c).
43,43
43,49
43,52
43,59
49,43
49,49
49,52
49,59
52,43
52,49
52,52
52,59
59,43
59,49
59,52
59,59
a. Find the median of each of the sixteen samples, then summarize the sampling distribution of the medians in the format of a table representing the probability distribution of the distinct median values. Use ascending order of the
sample medians.
Sample Median
Probability
Sample Median
Probability
(Type integers or simplified fractions. Use ascending order of the sample medians.)
p. Compare the population median to the mean of the sample medians. Choose the correct answer below.
O A. The population median is equal to half of the mean of the sample medians.
O B. The population median is not equal to the mean of the sample medians (it is also not half or double the mean of the sample medians).
OC. The population median is equal to the mean of the sample medians.
O D. The population median is equal to double the mean of the sample medians.
c. Do the sample medians target the value of the population median? In general, do sample medians make unbiased estimators of population medians? Why or why not?
O A. The sample medians target the population median, so sample medians are biased estimators, because the mean of the sample medians equals the population median.
O B. The sample medians do not target the population median, so sample medians are biased estimators, because the mean of the sample medians does not equal the population median.
OC. The sample medians do not target the population median, so sample medians are unbiased estimators, because the mean of the sample medians does not equal the population median.
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