Question

Consider the hypolhetreal population below, with population values: Unit Number 13 12 156 Chapter: Ratir and Regression Estimatiom Find the values of the population quantities t, iy, Sg, Sy, R, and B Construct a table like that in Table 4.2, giving the sampling distribution of Ny and of Ty, for a sample of size n 3. Draw a histogram of the sampling distribution of iyr. Compare this histogram a histogram of the sampling distribution of Nỹ. Find the mean and variance of the sampling distribution of îr. How do these compare to the mean and variance of Ny What is the bias of ir? Use Equation (4.6), together with the population quantities you calculated in (a) to tind an approximation to Bias (iyr) = NBias (i, ). How elose is the upproximation a C d to the true bias in (e)?

Answer 1

(au tx 13+7+ 11t 12+4+ 3+ 11+3 +5 There fore the value of t 69 G9 7.6667 1047+13+ 17 +8+1 +\5 7+4 -82 These fore, the alue of t 82 ty 2 -9.111 Y Sys 9-1 4.0924 The se fare, he value af S 18 4.0927 c0-9.1) +CA-9.111)+ -- + (4 9-1 S-1828 Therefore, the value f is s.1828 13.7.6604) Clo ~q.1111)++ (5-7.6661) Cy-7.1111) 927 XS-1828 138.333? co.gi52 CS Scained the edue of R t o.8152 CamScanner

B=ty 82 -1884 Thesefere the Valve f B 1884 Oing MINITAB,+he hesto gaum fer the Vaafable ty ghown beloa: Histogram of yy 16 l4- 1 2 80 85 9 95 100 l05 ho lis 120 S5 60 65 5c using MINITAB, the histogram f the Vafable Ng as shean below Htogram of tses 20- 15: 104 80 90 100 130 G0 TP we compaYe figuze t and figuze 2 ce ohseve that the histoypam also absesve that the xatlo estimatoy actually fearly mt las. e ittle a CS Soned withad aut CamScanner Rouanba

d By uing the Ms-Excel softane ommand Ave ag get the mean of the tyy es 2.7924 CNe Elcel Softanne Command Ag Also by using the Ms- get the vaa iance of the Sampling) dishibuton of 9 as 96. 9583 Cwe Similany, by wysng the MS Excel Softanae aunand Average get the mean of the to as 82. we Also by using ve leve taber od hy aing the MSEXcel Saftaane ommahd VAR digts butfan of fo as 89.3253 'we get the emping SRS The bas of t 82.79e4-82-0.19ey we ase gntetes ted to Computing appreti maHan to an Bias ( Ngf as )as tolloas Covnyputing the Cue Btasc Fay folleazy yo 3x.67 C-18u x165019-0.9152 x 4.09 27 x 5.1828) cantbaw e.furoe, ue get thie bias as CUP 0.O759 CS CamScanner