7. Assume a population of 46?, 51?, 53?, and 59. Assume thatsamples of size n=2 are randomly selected with replacement from thepopulation. Listed below are the sixteen different samples.Complete parts
?(a?) through (c?).
Sample x1 x2
1 46 46
2 46 51
3 46 53
4 46 59
5 51 46
6 51 51
7 51 53
8 51 59
9 53 46
10 53 51
11 53 53
12 53 59
13 59 46
14 59 51
15 59 53
- 59 59
a.Find the median of each of the sixteen? samples, thensummarize the sampling distribution of the medians in the format ofa table representing the probability distribution of the distinctmedian values. Use ascending order of the sample medians.
Social Median | Probability | Social Median | Probability |
(69,92,46) | | (78.5,105,52.5) | |
(71.5,97,48.5) | | (80.5,53,106) | |
(99,49.5,74) | | (110,55,82) | |
(76,102,51) | | (56,84.5,112) | |
(76.5,52,104) | | (88.5,118,59) | |
?(Type integers or simplified fractions. Use ascending order of thesample? medians.)
b. Compare the population median to the mean of the samplemedians. Choose the correct answer below.
A. The population median is equal to the mean of the samplemedians.
B. The population median is not equal to the mean of the samplemedians? (it is also not half or double the mean of the sample?medians).
C. The population median is equal to double the mean of thesample medians.
D. The population median is equal to half of the mean of thesample medians.
c. Do the sample medians target the value of the population?median? In? general, do sample medians make unbiased estimators ofpopulation? medians? Why or why? not?
A. The sample medians target the population? median, so samplemedians are unbiased? estimators, because the mean of the samplemedians equals the population median.
B. The sample medians target the population? median, so samplemedians are biased? estimators, because the mean of the samplemedians equals the population median.
C. The sample medians do not target the population? median, sosample medians are unbiased? estimators, because the mean of thesample medians does not equal the population median.
D. The sample medians do not target the population? median, sosample medians are biased? estimators, because the mean of thesample medians does not equal the population median.
