Question

A random sample of 496 U.S. adults are questioned regarding their political affiliation and opinion on a tax reform bill. The two categorical variables are political yffiliation and opinion on the tax reform bill. The observed contingency table is given below. Favor Indiferent Opposed Tota 82 63 150 Republican 6 83 146 496 14 Tota200 A) This sample has degree of freedom: DE If political affiliation and opinion on the tax retum bill are independent, then B) Accurate to 2 decimal places, the expected count in row 1 column 3 is E1,3 C) Accurate to 2 decimal places, the component vaiue in row 1 column 3 of the table is D) x value of this sample is E) At significance level 0.03, is the sample showing strong evidence that political affiliation and opinion on the tax reform bill are dependent? Use 4 decimal places for p-value. Yes No

Answer 1

Given Democrat Republican Total Favour IndifferentOpposed 82 68 150 137 63 200 63 83 146 Total 282 214 496 Expected values Indifferent 282 200/496 282*150/496282*146/496 -85.2823 214*200/496214 150/496 6214*146/496 EX Opposed -83.0081 2.9919 Favour Democrat 113.7097 Republican 86.2903 64.7177

Chi-square distribution table Observed Expected 137 82 63 63 68 83 113.7097 85.2823 83.0081 86.2903 64.7177 62.9919 (O-E)/E 4.7704 0.1263 4.8227 6.2862 0.1665 6.3551 22.5272 Test statistic r-s(OE )-22.527 a) Degrees of freedom DF=(r-1)(c-1) =(2-1)(3-1) =2 b) E1,3-83.0081 c) Component (1,3) -4.8227 d) Test statistic y2- d) Test statistic z-(0--22.527 2 e) Critical value-Xcritical-7.013 Since Test statistic x2> Critical value hence Reject the null hypothesis f) p-value-00000