Question

A recent study conducted in both Detroit and Salt Lake City asked single men in their twenties, “What sort of sporting event would you prefer to attend?” and gave them the three options below. Results of the survey are presented in the table. Conduct a test at the alpha=0.025 level to ascertain whether there is a difference in the pattern of responses between Detroit and Salt Lake City.

Vehicle	Detroit	Salt Lake City
Golf	10	40
Chess	40	10
Extreme Cycling	50	50

State Hypotheses:

Show work:

What is the value of the test statistic?

What is the value of the standard?

What is the result of the test?

Answer 1

Given table data is as below MATRIX col1 col2 TOTALS row 1 10 40 50 row 2 40 10 50 row 3 50 50 100 TOTALS 100 100 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 row 3 row3*col1/N row3*col2/N ------------------------------------------------------------------ expected frequecies calculated by applying E - table matrix formulae E-TABLE col1 col2 row 1 25 25 row 2 25 25 row 3 50 50 ------------------------------------------------------------------ calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above Oi Ei Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 10 25 -15 225 9 40 25 15 225 9 40 25 15 225 9 10 25 -15 225 9 50 50 0 0 0 50 50 0 0 0 ᴪ^2 o = 36 ------------------------------------------------------------------ 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 = 0.025 from standard normal table, chi square value at right tailed, ᴪ^2 α/2 =7.378 since our test is right tailed,reject Ho when ᴪ^2 o > 7.378 we use test statistic ᴪ^2 o = Σ(Oi-Ei)^2/Ei from the table , ᴪ^2 o = 36 critical value the value of |ᴪ^2 α| at los 0.025 with d.f (r-1)(c-1)= ( 3 -1 ) * ( 2 - 1 ) = 2 * 1 = 2 is 7.378 we got | ᴪ^2| =36 & | ᴪ^2 α | =7.378 make decision hence value of | ᴪ^2 o | > | ᴪ^2 α| and here we reject Ho ᴪ^2 p_value =0 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: 36 critical value: 7.378 p-value:0 decision: reject Ho

we have enough evidence to support the claim that  whether there is a difference in the pattern of responses between Detroit and Salt Lake City