Chi^2 Independence problem. A sample of 100 people is taken, and they are asked

Question

Chi^2 Independence problem. A sample of 100 people is taken, and they are asked about their reading habits for 2 publications, the Wall Street Journal, and Time magazine. 60% of the people read the Wall Street Journal, 45% of the people read Time, & 30% read both. Thus we have: a. Given the row& column totals, compute the 4 expected values for the rows & columns. b. How many degrees of freedom are there? c. Test whether reading the Wall Street Journal is independent of reading Time magazine for this dataset. Use alpha = 05.

Explanation / Answer

A) see the table above ,

Expected value in row corresponding to Ei

b) df = (r-1)(c-1) = 1

c) critical value = 3.84

TS = 1.5151

since

TS< critical value , we fail to reject the null hyothesis

and conclude that reading wall street journal is independent of reading Time magazine

c1 c2 total r1 30 15 45 r2 30 25 55 total 60 40 100 Oi 30 15 30 25 Ei 27 18 33 22 sum (O--Ei)^2/Ei 0.333333 0.5 0.272727 0.409091 1.515152 critical value 3.84

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