Question

A researcher wants to study the relationship between salary and gender. She randomly selects 215 individuals and determines their salary and gender. Can the researcher conclude that salary and gender are dependent? Male Female Total 22 20 42 23 20 43 Income Below $25,000 $25,000-$50,000 $50,000-$75,000 Above $75,000 Total 31 34 65 34 31 65 110 105 215 Copy Data Prev Next Step 2 of 8: Find the expected value for the number of men with an income below $25,000. Round your answer to one decimal place

Answer 1

Given table data is as below MATRIX col1 col2 TOTALS row 1 22 20 42 row 2 23 20 43 row 3 31 34 65 row 4 34 31 65 TOTALS 110 105 215 ------------------------------------------------------------------ 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 formula E-TABLE col1 col2 row 1 21.488 20.512 row 2 22 21 row 3 33.256 31.744 row 4 33.256 31.744 ------------------------------------------------------------------ calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above Oi Ei Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 22 21.488 0.512 0.262 0.012 20 20.512 -0.512 0.262 0.013 23 22 1 1 0.045 20 21 -1 1 0.048 31 33.256 -2.256 5.09 0.153 34 31.744 2.256 5.09 0.16 34 33.256 0.744 0.554 0.017 31 31.744 -0.744 0.554 0.017 ᴪ^2 o = 0.465 ------------------------------------------------------------------ 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 =7.815 since our test is right tailed,reject Ho when ᴪ^2 o > 7.815 we use test statistic ᴪ^2 o = Σ(Oi-Ei)^2/Ei from the table , ᴪ^2 o = 0.465 critical value the value of |ᴪ^2 α| at los 0.05 with d.f (r-1)(c-1)= ( 4 -1 ) * ( 2 - 1 ) = 3 * 1 = 3 is 7.815 we got | ᴪ^2| =0.465 & | ᴪ^2 α | =7.815 make decision hence value of | ᴪ^2 o | < | ᴪ^2 α | and here we do not reject Ho ᴪ^2 p_value =0.927 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: 0.465 critical value: 7.815 p-value:0.927 decision: do not reject Ho

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

Expected value for the number of men with an income below 25000$ is 21.5