Question

AUDIENCE

MADE ME WANT TO VISIT THE BRAND WEBSITE

Yes

No

Total

Podcast (Internet Radio)

196

98

294

Traditional Radio

135

104

239

a. Set up the null and alternative hypotheses to try to determine whether ad impact is different following Podcast listening than following Traditional Radio listening. Set Podcast audience as population 1.

H0:

H1:

b. State which test is used for testing your hypothesis in part a.

c. What is the test statistic of the hypothesis test in part a? Keep at least 2 decimal places. Show work. A loss of marks will result for not showing work even if your answer is correct.

Test Statistic

d. Compute the p-value and interpret its meaning. Keep at least 4 decimal places. Show work. A loss of marks will result for not showing work even if your answer is correct.

p-Value

e. What are the decision and the conclusion of the test based on your answer in part d assuming 0.01 level of significance? Explain how you made the decision.

Decision:

Conclusion:

Answer 1

Given table data is as below MATRIX col1 col2 TOTALS row 1 196 98 294 row 2 135 104 239 TOTALS 331 202 N = 533 ------------------------------------------------------------------ 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 1 182.578 111.422 row 2 148.422 90.578 ------------------------------------------------------------------ calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above Oi Ei Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 196 182.578 13.422 180.15 0.987 98 111.422 -13.422 180.15 1.617 135 148.422 -13.422 180.15 1.214 104 90.578 13.422 180.15 1.989 ᴪ^2 o = 5.807 ------------------------------------------------------------------ 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 =6.635 since our test is right tailed,reject Ho when ᴪ^2 o > 6.635 we use test statistic ᴪ^2 o = Σ(Oi-Ei)^2/Ei from the table , ᴪ^2 o = 5.807 critical value the value of |ᴪ^2 α| at los 0.01 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 2 - 1 ) = 1 * 1 = 1 is 6.635 we got | ᴪ^2| =5.807 & | ᴪ^2 α | =6.635 make decision hence value of | ᴪ^2 o | < | ᴪ^2 α | and here we do not reject Ho ᴪ^2 p_value =0.016 ANSWERS --------------- a. 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 b. chi square test for independent c. test statistic: 5.807 critical value: 6.635 d. p-value:0.016 decision: do not reject Ho

e. we do not have enough evidence to support the claim that  whether ad impact is different following podocast listening than following traditional radio listening