# 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

https://brainmass.com/statistics/chi-squared-test/15-19-students-who-finish-exam-15-25-forecasters-interest-319292

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