Question

# Markets have become interested in the potential of social networking sites. But they need to understand...

Markets have become interested in the potential of social networking sites. But they need to understand the demographics of social networking users. A research company conducted a survey in late 2012 that asked about social networking over several years and for different age groups. A table of responses is shown to the right

May 2010 Aug 2011 Aug 2012 total

18-29 274 280 309 863

30-49 323 352 379 1054

50-64 258 282 321 861

Total 855 914 1009 2778

-----The expected values are:

18-29: 265.61 283.94 313.45

30-49 324.40 346.78 382.82

50-64 264.99 283.28 312. 72

a) Compute the x2 statistic

b) How many degree of freedom foes x2 statistic have?

c) Find the critical value where alpha = 0.05

applying chi square test on above data:

 Observed OBS may -2000 aug-2011 aug-2012 Total 18-29 274 280 309 863 30-49 323 352 379 1054 50-64 258 282 321 861 Total 855 914 1009 2778 Expected Ei=?row*?column/?total may -2000 aug-2011 aug-2012 Total 18-29 265.610 283.940 313.450 863 30-49 324.400 346.780 382.820 1054 50-64 264.990 283.280 312.720 860.99 Total 855 914 1008.99 2777.99 chi square =(Oi-Ei)2/Ei may -2000 aug-2011 aug-2012 Total 18-29 0.27 0.05 0.06 0.38 30-49 0.01 0.079 0.038 0.12 50-64 0.18 0.006 0.219 0.41 Total 0.46 0.14 0.32 0.915

a) x2 statistic =0.915

b)degree of freedom =(rows-1)*(column-1)=(3-1)*(3-1)=4

c) for 4 df and 0.05 level critical value =9.488

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