Question

Question I. A random sample of 75 cities has been classified as small or large by population and as high or low on crime rate. Based on information below, identify and interpret the strength, pattern/direction, PRE, and significance of the association between the dependent and independent variable at the alpha level of 0.05. Show five steps if relevant. Obtain all the relevant statistics. Provide a brief overall conclusion. (10 marks) Crime rate by city size City size Crime rate Small Large Total Low 45 10 55 High 10 10 20 Total 55 20 75 BH

Answer 1

1.

Given table data is as below MATRIX col1 col2 TOTALS row 1 45 10 55 row 2 10 10 20 TOTALS 55 20 N = 75 ------------------------------------------------------------------ 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 formulae E-TABLE col1 col2 row 1 40.333 14.667 row 2 14.667 5.333 ------------------------------------------------------------------ calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above Oi Ei Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 45 40.333 4.667 21.781 0.54 10 14.667 -4.667 21.781 1.485 10 14.667 -4.667 21.781 1.485 10 5.333 4.667 21.781 4.084 ᴪ^2 o = 7.594 ------------------------------------------------------------------ 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 =3.841 since our test is right tailed,reject Ho when ᴪ^2 o > 3.841 we use test statistic ᴪ^2 o = Σ(Oi-Ei)^2/Ei from the table , ᴪ^2 o = 7.594 critical value the value of |ᴪ^2 α| at los 0.05 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 2 - 1 ) = 1 * 1 = 1 is 3.841 we got | ᴪ^2| =7.594 & | ᴪ^2 α | =3.841 make decision hence value of | ᴪ^2 o | > | ᴪ^2 α| and here we reject Ho ᴪ^2 p_value =0.006 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: 7.594 critical value: 3.841 p-value:0.006 decision: reject Ho

we have enough evidence to support the claim that there is association between dependent and independent variable.