Discussion:
Q1: 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 a= .10, is the grade independent of the order handed in? Since it is a 2*2 table, try also a two-tailed two-sample z test for π1= π2 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
Q2: Forecasters' interest rate predictions over the period 1982-1990 were studied to see whether the predictions corresponded to what actually happened. The 2 * 2 contingency table below shows the frequencies of actual and predicted interest rate movements. Research question: At a = .10, is the actual change independent of the predicted change?
How Well Do Analysts Forecast Interest Rates?
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