Question

Suppose the House of Representatives had a recent vote. The President praised it, saying that everyone involved voted independently of party. Is this true? I have entered in the numbers I got using the formula from the chi-square statistic. voted yes Republican Democrat Independent 0.44 0.19 0.35 0.13 0.50 0.46 voted no abstained from voting 0.71 0.06 5.93 What is the chi-square value? [Select) [Select) What is the p-value? [Select] 0.44 0.71 8.77 45.11

same questions with drop down options.

Answer 1

7.

Given table data is as below MATRIX col1 col2 col3 TOTALS row 1 0.44 0.19 0.35 0.98 row 2 0.13 0.5 0.46 1.09 row 3 0.71 0.06 5.93 6.7 TOTALS 1.28 0.75 6.74 N = 8.77 ------------------------------------------------------------------ calculation formula for E table matrix E-TABLE col1 col2 col3 row 1 row1*col1/N row1*col2/N row1*col3/N row 2 row2*col1/N row2*col2/N row2*col3/N row 3 row3*col1/N row3*col2/N row3*col3/N ------------------------------------------------------------------ expected frequencies calculated by applying E - table matrix formulae E-TABLE col1 col2 col3 row 1 0.143 0.084 0.753 row 2 0.159 0.093 0.838 row 3 0.978 0.573 5.149 ------------------------------------------------------------------ calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above Oi Ei Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 0.44 0.143 0.297 0.088 0.615 0.19 0.084 0.106 0.011 0.131 0.35 0.753 -0.403 0.162 0.215 0.13 0.159 -0.029 0.001 0.006 0.5 0.093 0.407 0.166 1.785 0.46 0.838 -0.378 0.143 0.171 0.71 0.978 -0.268 0.072 0.074 0.06 0.573 -0.513 0.263 0.459 5.93 5.149 0.781 0.61 0.118 ᴪ^2 o = 3.574 ------------------------------------------------------------------ set up null vs alternative as null, Ho: no relation b/w X and Y OR X and Y are independent alternative, H1: exists a relation b/w X and Y OR X and Y are dependent level of significance, α = 0.05 from standard normal table, chi square value at right tailed, ᴪ^2 α/2 =9.488 since our test is right tailed,reject Ho when ᴪ^2 o > 9.488 we use test statistic ᴪ^2 o = Σ(Oi-Ei)^2/Ei from the table , ᴪ^2 o = 3.574 critical value the value of |ᴪ^2 α| at los 0.05 with d.f (r-1)(c-1)= ( 3 -1 ) * ( 3 - 1 ) = 2 * 2 = 4 is 9.488 we got | ᴪ^2| =3.574 & | ᴪ^2 α | =9.488 make decision hence value of | ᴪ^2 o | < | ᴪ^2 α | and here we do not reject Ho ᴪ^2 p_value =0.467 ANSWERS --------------- null, Ho: no relation b/w X and Y OR X and Y are independent alternative, H1: exists a relation b/w X and Y OR X and Y are dependent test statistic: 3.574 critical value: 9.488 p-value:0.467 p value is greater than alpha vale decision: do not reject Ho

we do not have enough evidence to support the claim that there is association of everyone invoved independent

of party