Question

A research study found the following sample data regarding preferred pace of life and gender:

                                                                                                Gender

Preferred Pace of Life                                      Male                                      Female

Slower                                                                  230                                         218

No Preference                                                  20                                           24

Faster 90                                           48

Test to see if Preferred Pace of Life is independent of Gender. Assume α = 0.01.

What is the expected frequency for No Preference and Female if the variables are independent?

How many degrees of freedom are in the test?

What is the critical value of the test statistic?

What is the p-value?

What is your decision about the null and your conclusion?

Answer 1

Given table data is as below MATRIX col1 col2 TOTALS row 1 230 218 448 row 2 20 24 44 row 3 90 48 138 TOTALS 340 290 N = 630 ------------------------------------------------------------------ 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 ------------------------------------------------------------------ expected frequecies calculated by applying E - table matrix formulae E-TABLE col1 col2 row 1 241.778 206.222 row 2 23.746 20.254 row 3 74.476 63.524 ------------------------------------------------------------------ calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above Oi Ei Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 230 241.778 -11.778 138.721 0.574 218 206.222 11.778 138.721 0.673 20 23.746 -3.746 14.033 0.591 24 20.254 3.746 14.033 0.693 90 74.476 15.524 240.995 3.236 48 63.524 -15.524 240.995 3.794 ᴪ^2 o = 9.561 ------------------------------------------------------------------ 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 = 0.01 from standard normal table, chi square value at right tailed, ᴪ^2 α/2 =9.21 since our test is right tailed,reject Ho when ᴪ^2 o > 9.21 we use test statistic ᴪ^2 o = Σ(Oi-Ei)^2/Ei from the table , ᴪ^2 o = 9.561 critical value the value of |ᴪ^2 α| at los 0.01 with d.f (r-1)(c-1)= ( 3 -1 ) * ( 2 - 1 ) = 2 * 1 = 2 is 9.21 we got | ᴪ^2| =9.561 & | ᴪ^2 α | =9.21 make decision hence value of | ᴪ^2 o | > | ᴪ^2 α| and here we reject Ho ᴪ^2 p_value =0.008 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: 9.561 critical value: 9.21 p-value:0.008 decision: reject Ho

we have enough evidence to support the claim that   if Preferred Pace of Life is independent of Gender