Question

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

Answer 1

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