Question

Assume a population of 1, 4, and 10. Assume that samples of size n = 2 are randomly selected with replacement from the population. Listed below are the nine different samples. Complete parts a through d below. 1,1 1,4 1,10 4,1 4,4 4,10 10,1 10,4 10,10 o a. Find the value of the population standard deviation o. (Round to three decimal places as needed.) b. Find the standard deviation of each of the nine samples, then summarize the sampling distribution of the standard deviations in the format of a table representing the probability distribution of the distinct standard deviation values. Use ascending order of the sample standard deviations. Probability (Type integers or fractions.) c. Find the mean of the sampling distribution of the sample standard deviations. The mean of the sampling distribution of the sample standard deviations is | (Round to three decimal places as needed.) d. Do the sample standard deviations target the value of the population standard deviation? In general, do sample standard deviations make good estimators of population standard deviations? Why or why not? O A. The sample standard deviations do target the population standard deviation, therefore, sample standard deviations are biased estimators. O B. The sample standard deviations do not target the population standard deviation, therefore, sample standard deviations are biased estimators. O C. The sample standard deviations do target the population standard deviation, therefore, sample standard deviations are unbiased estimators. OD. The sample standard deviations do not target the population standard deviation, therefore, sample standard deviations are unbiased estimators.

Answer 1

Pano Answer:- Given that, population - 1, 4, 10 Population size = 3 (N) a) population Standard deviation co E- Formula: Here, X 1 , 410 X- 1+4+10 3 -15 8 = 5 Substitute values in above Formula G J11-5;8+ [4-538+(10-512 3 v 1984 (0%4132

PINCTR) - पर - 3,7416 30241 b) Standard deviation of nine samples. Sample sample sampleman | Sample variance Sample Standard 1 - deviation [ (5२. (X-D9 6:- n- 14141 २ 4.5 40.5 2.11320 45 पति - ५ (1) (14) ।।५:25 (110) 40-5.5 1471) in : 2.5 (५५) (40) ५३० - 7 (10)1) 11 : 5.5 ८1०५) tc५:१ (10,10) | Ictic = 10 using above table 5 0- of-पाप२ २.1213 6.363961 2.11320 0.0000 ५.२५2646 6.36396) 4.३५२640 0.0000 ५.३५६66 .3639/

Pag No © P15-5): Number of samples having s:D equal to s Tolai no of Samples c) Mean sampling distribution :- of sample standard Mean deviation Sampling distribution is £(5) - Es. P25-5) = {oxes] +(1.4149733421219x&]+[4.9426x?] xf6 237 - 0+0:15713 +0.4914 +0.9488 +1.424.8 65): 2.9857 mean of sampling distribertion of sample standard deviation is 2.985 The sample - Standard deviations do not target the population Standard deviation; therefore sample Standard deviations are biased estimators. . Hence, option ő is correct. d)