Markets have become interested in the potential of social networking sites. But
ID: 3252303 • Letter: M
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. Under the usual null hypothesis, what are the expected values? Complete the table below. Compute the xi^2 statistic. xi^2 = _____ (Round to two decimal places as needed.) How many degrees of freedom does the xi^2 statistic have? Df = ___ (Type an integer or a decimal.) What do you conclude? Find the critical value for alpha = 0.05.Explanation / Answer
a) The counts and their respective expected counts are given below:
May 2010 Aug 2011 Aug 2012 All
18-29 266 282 302 850
256.6 285.6 307.9
30-49 318 370 381 1069
322.7 359.2 387.2
50-64 256 283 325 864
260.8 290.3 312.9
All 840 935 1008 2783
Cell Contents: Count
Expected count
b) The Chi-square statistic is given as: 1.73
c) The Chi-square statistic has 4 degrees of freedom.
d) The p-value of this test is 0.785. Thus at 5% l.o.s. we accept the hypothesis and conclude that there is no association in the data over the different years.