Question

A researcher wants to study the relationship between salary and gender. She randomly selects 324 individuals and determines their salary and gender. Can the researcher conclude that salary and gender are dependent? Total Male Female 26 24 50 Income Below $25,000 $25,000-$50,000 $50,000-$75,000 Above $75,000 38 72 42 47 89 53 60 113 Total 155 169 324 < "rev Copy Data

Answer 1

Given table data is as below MATRIX col1 col2 TOTALS row 1 26 24 50 row 2 34 38 72 row 3 42 47 89 row 4 53 60 113 TOTALS 155 169 324 ------------------------------------------------------------------ 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 row 3 row3*col1/N row3*col2/N row 4 row4*col1/N row4*col2/N ------------------------------------------------------------------ expected frequencies calculated by applying E - table matrix formulae E-TABLE col1 col2 row 1 23.92 26.08 row 2 34.444 37.556 row 3 42.577 46.423 row 4 54.059 58.941 ------------------------------------------------------------------ calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above Oi Ei Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 26 23.92 2.08 4.326 0.181 24 26.08 -2.08 4.326 0.166 34 34.444 -0.444 0.197 0.006 38 37.556 0.444 0.197 0.005 42 42.577 -0.577 0.333 0.008 47 46.423 0.577 0.333 0.007 53 54.059 -1.059 1.121 0.021 60 58.941 1.059 1.121 0.019 ᴪ^2 o = 0.413 ------------------------------------------------------------------ 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 = 0.1 from standard normal table, chi square value at right tailed, ᴪ^2 α/2 =6.251 since our test is right tailed,reject Ho when ᴪ^2 o > 6.251 we use test statistic ᴪ^2 o = Σ(Oi-Ei)^2/Ei from the table , ᴪ^2 o = 0.413 critical value the value of |ᴪ^2 α| at los 0.1 with d.f (r-1)(c-1)= ( 4 -1 ) * ( 2 - 1 ) = 3 * 1 = 3 is 6.251 we got | ᴪ^2| =0.413 & | ᴪ^2 α | =6.251 make decision hence value of | ᴪ^2 o | < | ᴪ^2 α | and here we do not reject Ho ᴪ^2 p_value =0.938 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: 0.413 critical value: 6.251 p-value:0.938 decision: do not reject Ho

we do not have enough evidence to support the claim that there is a relationship between income and gender.