3. Testing for equal proportions tmagine that you are contracted by a local news

Question

3. Testing for equal proportions tmagine that you are contracted by a local news provider to study consumer demographics in relatian to three different types of news media: print (newspaper), Internet, and television. In priar market research, the company has dassified each of its customers as receiving news content primariy from only one of these three sources, and as either urban or rural residents. In arder to help design effective marketing strategies, yau are asked to perform a test for equality of proportions to determine whether there is a significant difference in the propartion af consumers who live in urban versus rural areas for the three media types that are affered. The three population proportions that you are interested in are: P1proportion of urban consumers for the population of newspaper readers P2 proportion of urban consumers for the population of Intermet news readers Ps proportion of urban consumers for the population of Tv news consumers You conduct a hypothesis test with a.01 level of significance to determine whether the praportion of urban consumers is the same for all three news sources The null and altemate hypatheses for yaur test are: Hpl Ha: You collect a random sample of 1,232 consumers of the company's news content. You find that 227 of the 330 newspaper consumers, 313 of the 445 Internet consumers, and 348 of the 457 TV consumers lived in urban areas. The data are summarized in the following able: sample Results Newspaper Internet TV Total 313 consumer Urban 227 Rura 103 330 109 344 445 457 1,232 complete the following table of expected frequencies for each population, assuming Ho is true (round the frequencies to the nearest whole number). (Note: Due to rounding, the row and column totals for your version of this problem may not match the values shown in the table.) 10:37 PM ^4x 10/25/2017 Type here to search

Explanation / Answer

H0 : Proportions of print, electronic and internet media is same for rural and urban area. p1 = p2 = p3

Ha : Proportions of print, electronic and internet media is different for rural and urban area.p1 p2 p3

Observed Table

Expected Frequency

Expected Value for Urban - Newspaper = Total Urban People * Total Newspaper/ Total people

= 888 * 330/ 1232 = 237.85

similarly, we will calculate

CHi - square value

X2 = (Oi - Ei)2 /Ei

X2 = 6.21

so from table critical value for dF = 2

X2cr = X2 0.01,2 = 9.210

so X2 < X2cr

so we shall not reject the null hypothesis and can conclude that Proportions of print, electronic and internet media is same for rural and urban area. p1 = p2 = p3

News Source Newspaper Internet TV Total Consumer Urban 227 313 348 888 Rural 103 132 109 344 total 330 445 457 1232

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