Question 6.EX.3: (a) Verify the claim in the worked example above, that both ...
(a) Verify the claim in the worked example above, that both \chi^2 and z statistic methods give the same qualitative (accept or reject) result when the observed frequencies are 16, 55, 29 and when they are 14, 55, 31.
(b) In each case, look up or calculate (using Excel) the Prob-values for the \chi^2 and z test statistics and compare.
The test statistics are for (16, 55, 29) \chi^2 = 4.38 (Prob-value = 0.112) and z = 1.84 (Prob-value = 0.066) and for (14, 55, 31) \chi^2 = 6.78 (Prob-value = 0.038) and z = 2.40 (Prob-value = 0.016). The two methods agree on the results, although the Probvalues are quite different.
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