Question

QUESTION 3

1. A research firm is conducting a study to determine if there is a relationship between an individual’s age and the individual’s preferred source of news. The research firm asked 1,000 individuals to list their preferred source for news: newspaper, radio and television, or the Internet. The following results were obtained:

   Individual News Preference

   Preferred News Source	Age of Respondent
   	20-30	31-40	41-50	Over 50
   Newspaper	19	62	95	147
   Radio/TV	27	125	168	88
   Internet	104	113	37	15

   At the 0.01 level of significance, can the research firm conclude that there is a relationship between the age of the individual and the individual’s preferred source of news.

Answer 1

3.

Given table data is as below MATRIX col1 col2 col3 col4 TOTALS row 1 19 62 95 147 323 row 2 27 125 168 88 408 row 3 104 113 37 15 269 TOTALS 150 300 300 250 N = 1000 ------------------------------------------------------------------ calculation formula for E table matrix E-TABLE col1 col2 col3 col4 row 1 row1*col1/N row1*col2/N row1*col3/N row1*col4/N row 2 row2*col1/N row2*col2/N row2*col3/N row2*col4/N row 3 row3*col1/N row3*col2/N row3*col3/N row3*col4/N ------------------------------------------------------------------ expected frequencies calculated by applying E - table matrix formulae E-TABLE col1 col2 col3 col4 row 1 48.45 96.9 96.9 80.75 row 2 61.2 122.4 122.4 102 row 3 40.35 80.7 80.7 67.25 ------------------------------------------------------------------ calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above Oi Ei Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 19 48.45 -29.45 867.303 17.901 62 96.9 -34.9 1218.01 12.57 95 96.9 -1.9 3.61 0.037 147 80.75 66.25 4389.06 54.354 27 61.2 -34.2 1169.64 19.112 125 122.4 2.6 6.76 0.055 168 122.4 45.6 2079.36 16.988 88 102 -14 196 1.922 104 40.35 63.65 4051.32 100.405 113 80.7 32.3 1043.29 12.928 37 80.7 -43.7 1909.69 23.664 15 67.25 -52.25 2730.06 40.596 ᴪ^2 o = 300.532 ------------------------------------------------------------------ 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 =16.812 since our test is right tailed,reject Ho when ᴪ^2 o > 16.812 we use test statistic ᴪ^2 o = Σ(Oi-Ei)^2/Ei from the table , ᴪ^2 o = 300.532 critical value the value of |ᴪ^2 α| at los 0.01 with d.f (r-1)(c-1)= ( 3 -1 ) * ( 4 - 1 ) = 2 * 3 = 6 is 16.812 we got | ᴪ^2| =300.532 & | ᴪ^2 α | =16.812 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: 300.532 critical value: 16.812 p-value:0 decision: reject Ho

we have enough evidence to support the claim that   the research firm conclude that there is a relationship between the age of the individual and the individual’s preferred source of news.