Question

1. Use a χ² test to test the claim that in the given contingency table, the row variable and the column variable are independent.

Responses to a survey question are broken down according to employment status and the sample results are given below. At the 0.10 significance level, test the claim that response and employment status are independent.

a. find the test statistic

2. Use a χ² test to test the claim that in the given contingency table, the row variable and the column variable are independent.

Tests for adverse reactions to a new drug yielded the results given in the table. At the 0.05 significance level, test the claim that the treatment (drug or placebo) is independent of the reaction (whether or not headaches were experienced).

a. Find the test statistic

Answer 1

Solution 0. Responses to a to employment suney status question are broken and the sample down results according below. Total 30 = Employed unemployed Total yes 30 20 I so no 15 25 40 undecided 5 10 IS 5 I L 5 N=105 The Ho : null The and alternative hypotheso is, response and employment status are independent. VS. Hi The response and employment status are dependent. Here, Then we have to use chi-square rest of independency. expected frequency table below (eij). Yes NO Total Employed soso undecided sox15 - 105 = 7.1428 SoxGO los = 16,0476 105 = 23.8095 unemployed SSXIS 105 I SS SSXSO los = 26.1904 so SSX 40 105 = 20.9523 I 40 =7.8571 15 L I Total I N=105 Here, oig = observed frequency of (ij) is, tos ie .N= 105 Then table for ej? bij ie oj 2

INO undecided 2 Total Employed Yes 302 23.8095 IS? 52 19,0476 7.1428 53.1125 → 37.8000 - 11. 8125 T = 3.5ooo unemployed 25 To 2 202 26.1904 20.9523 7.8571 57.8296 = 18,2727 5310727 = 29,8296 41.6421 = 12.7273 16.2273 Total el 110.942 Then test statistics becomes, x² = q qoij? - N = 110.9421 - 105 x² = sigual | it. Xeel = sigual Critical value is, Xenitical = x² will dof at a=0.10 devel of significance. = x²(3-1) (2-1) def = XE2) dif at a=0.10 Tx critical = 4.605 it. X coul> 2² mitical we Then are reject the we conclude dependent null that hypothesis. the response and employment status Solution - ② drug yielded Tests the for results adverse given reactions to a new in the table.

Doug Headaches aall No headaches 6=73 Total a+c=84 Placebo b=7 d=91 bed=98 Total ato = 18 cod = 164 N = 182 The Ho : null The hypothesis is independent of and alternative treatment is vs. treatment is the reaction. : The dependent of the reaction. The chi-square test statistics is x² = N (ad bc) 2 Catb) (arc) (c+d) (bord) 182 [(11) (91)-(2)(732) ? (18) (84) (164) (98) T22 = 1.7992 I I ie krecel = 1.7982 X critical = x²1 d.f at d=0,05 level of significance [x²rtical = 3.841 i. 2²cl < x²ritical we accept null hypothesis. Then we conclude the reaction. that the treatment is inclependent of