Question

A researcher wants to study the relationship between salary and gender. She randomly selects 306 individuals and determines their salary and gender. Can the researcher conclude that salary and gender are dependent? Total Male Female 28 31 59 70 36 Income Below $25,000 $25,000-$50,000 $50,000-$75,000 Above $75,000 Total 45 88 43 41 48 89 155 151 306 > Step 4 of 8: Find the value of the test statistic. Round your answer to three decimal places Prev Tables Keyboard Shortcuts Answer to Enter Point

Answer 1

use 45 88 Solno. To check independence of the salary and gender we chi-square test: The table of observed frequencies: Income Male Female Total Below $ 25,000 31 59 $25,000 - $59000 34 36 70 $50,000 - $75,000 43 Above $75,000 48 41 89 155 Total 151 306 =N where N = Total observations. Now, we compute the table of expected frequencies; We know, eij Rix C; Expected frequency of cujuth cell N ith row where = Ri total Cj = jth column total. Thus eu 29.85 29.11 59 x 155 306 ele 59 X 151 306 35.46 eal 34, 54 222 = Fox 155 306 = 70 X 151 306 44,57 es = 88 X 155 306 ,932 43.42 88 x 151 306 eal 45.08 e4a= 89 X 155 306 43. 91 898151 306 Female 29.01 Hence, Table of expected frequency : Income Male Below $25,000 29.85 $25,000-$50,000 35.46 $50,000 - $75,000 44,57 Above $75,000 45.08 34, 54 43, 42 43. 31 CS Scanned with CamScanner

Hypothesis to be tested; Hai Salary and gender of a person is independent He: Salary and gender of person is not independenta test statistic is given by Then chi-square X ¿ CO-ED? HER-UCC-1) ca i1 E TR-120C-1) where o observed frequency Expected frequency R: Total rows & Ci Total columns Thus, using previous two table we compute Xian (28-29.85)2 + ( 34-35.46)2+(45–44.57) + (48-45.08) 29.85 35.46 45.08 + (31- 29.11)? + (36 - 34.54)? +(43-43. 42)+ (41- 43.9112 29.11 34.54 43.4.3 43.31 44.57 (२.१२)२ 45.08 + (1.89) ? (1-4602 29.11 34.54 (-1.850 (-1.4602 (0.43D2 29.85 35.46 44.57 (-0.402 (-2.9109 43.42 43.91 = 0.114.7 + 0.0601 + 0.0041 +0.1891 + 0.1227 +0.0617 +0.0040+0.1999 .: Real. - Xžalo =_0.7493 " Answer 0.749 CS Scanned with CamScanner

7. 815 . Answer 0.749 Now, we find Xoritical Xeniticee value from chi-square table with CR-1) CC-1) = 3x1=3 degrees of freedom, when x=0.05 a criticat From table. Since x < Xical there strong evidence to accept hy pothesia .. we that say Salary and gender of a person is independent is con CS Scanned with CamScanner