Question

A recent study was conducted to determine whether there was a relationship between work (X) and education (Y) where 200 people were asked two questions:
1) Are you educated? 2) Are you engaged in what?) The answer should be yes or no.
Required: Calculate the coefficient of association with interpretation of the results.

	education	no education
work	113	23
no work	49	15

Answer 1

Given table data is as below MATRIX col1 col2 TOTALS row 1 113 23 136 row 2 49 15 64 TOTALS 162 38 N = 200 ------------------------------------------------------------------ calculation formula for E table matrix E-TABLE col1 col2 row 1 row1*col1/N row1*col2/N row 2 row2*col1/N row2*col2/N ------------------------------------------------------------------ expected frequencies calculated by applying E - table matrix formula E-TABLE col1 col2 row 1 110.16 25.84 row 2 51.84 12.16 ------------------------------------------------------------------ calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above Oi Ei Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 113 110.16 2.84 8.066 0.073 23 25.84 -2.84 8.066 0.312 49 51.84 -2.84 8.066 0.156 15 12.16 2.84 8.066 0.663 chisqr^2 o = 1.204 ------------------------------------------------------------------ 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, alpha = 0.05 from standard normal table, chi square value at right tailed, chisqr^2 alpha/2 =3.841 since our test is right tailed,reject Ho when chisqr^2 o > 3.841 we use test statistic chisqr^2 o = Σ(Oi-Ei)^2/Ei from the table , chisqr^2 o = 1.204 critical value the value of |chisqr^2 alpha| at los 0.05 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 2 - 1 ) = 1 * 1 = 1 is 3.841 we got | chisqr^2| =1.204 & | chisqr^2 alpha | =3.841 make decision hence value of | chisqr^2 o | < | chisqr^2 alpha | and here we do not reject Ho chisqr^2 p_value =0.273 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: 1.204 critical value: 3.841 p-value:0.273 decision: do not reject Ho

1.

yes,

educated

2.

no,

engaged

we do not have enough evidence to support the claim that   whether there was a relationship between work (X) and education (Y)