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# 15.19 Students who finish exam ; 15.25 Forecasters' Interest

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15.19 To see whether students who finish an exam first get the same grades as those who finish later, a professor kept track of the order in which papers were handed in. Of the first 25 papers, 10 received a B or better compared with 8 of the last 24 papers handed in. Research question: At? = .10, is the grade independent of the order handed in? Since it is a 2 Ã- 2 table, try also a two-tailed two-sample z test for Ï?1 = Ï?2 (see Chapter 10) and verify that z2 is the same as your chi-square statistic. Which test do you prefer? Why?

Grade Earlier Hand-In Later Hand-In Row Total
or better 10 8 18
or worse 15 16 31
Col Total 25 24 49

15.25 Forecasters' interest rate predictions over the period 1982-1990 were studied to see whether the predictions corresponded to what actually happened. The 2 Ã- 2 contingency table below shows the frequencies of actual and predicted interest rate movements. Research question: At ? = .10, is the actual change independent of the predicted change? (Data are from R. A. Kolb and H. O. Steckler, â??How Well Do Analysts Forecast Interest Rates?â? Journal of Forecasting 15, no. 15 [1996], pp. 385-394.)

Forecasted Change Rates Fell Rates Rose Row Total
Rates would fall 7 12 19
Rates would rise 9 6 15
Col Total 16 18 34

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