Question

Consider a family of four people, aged 8, 10, 33, and 37 as a population a) Calculate the population variance and standard deviation for the ages. Show your work step by step b) Random samples of size two are drawn with replacement from this population and their ages are recorded Find the variance and standard deviation for each sample (using the formula that involves divisions by n-1) and fill in the 3rd and 4th columns of the table Find the variance and standard deviation for each sample by treating the sample as a population (using the formula that involves divisions by n) and fill in the 5th and 6th columns of the table Find the mean for each column and list them in the last row of the table Sample Sample Values SD (treated as a VAR (treated as a VAR (treated as a sample SD (treated as a sample opulation opulation 8,8 8,10 8,33 8,37 10,8 10,10 10,33 10,37 33,8 33,10 33,33 33,37 37,8 37,10 37,33 37,37 4 10 12 13 14 15 16 Mean- Mean- Mean- Mean- mean is equal to the population parameter, the statistic is said to be an unbiased estimator of that parameter Which method (dividing by n-1 or dividing by n or neither) resulted in an unbiased estimate of the population variance? Make sure to justify your answer to get full credit.

Answer 1

Page No. Date oa ford Dlvia 1.4192) 12 7.6777) 312.5 1. A3 56.25 210.24 2 10 JO 10 336.263 21.5 03719099 3 8/2 677732.5 33,10 3323 32.25 482.25 5625 9.5 | 21% |/6, 2639 | IL 」2 2/0.25 22 25 /4-5 1 요 15-t-37-33- 2.1289 6.875 \ 85.75 9.7217)」71 :5 leon