We saw in Part II Review Exercise R2.21 that Old Faithful eruptions do not occur at constant intervals and the intervals may vary greatly. In that exercise, we fit a regression model, which we can now improve with t- statistics and P-values.

a) State and test the natural null hypothesis for the slope.

Here are summary statistics for the variables:

b) Create a 95% confidence interval for the mean length of time that will elapse following a 2-minute eruption.
c) You arrive at Old Faithful just as an eruption ends. Witnesses say it lasted 4 minutes. Create a 95% prediction interval for the length of time you should expect to wait to see the next eruption.

Data From Exercise R5.21

Several programs attempt to address the shortage of qualified teachers by placing uncertified instructors in schools with acute needs—often in inner cities. A study compared students taught by certified teachers to others taught by uncertified teachers in the same schools. Reading scores of the students of certified teachers averaged 35.62 points with standard deviation 9.31. The scores of students instructed by uncertified teachers had mean 32.48 points with standard deviation 9.43 points on the same test. There were 44 students in each group. The appropriate t-procedure has 86 degrees of freedom. Is there evidence of lower scores with uncertified teachers? Discuss. (The Effectiveness of “Teach for America” and Other Under-certified Teachers on Student Academic Achievement: A Case of Harmful Public Policy. Education Policy Analysis Archives)

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Dependent variable is Interval R-squared = 77.0% s = 6.159 with 222 2 220 degrees of freedom Variable Coefficient Intercept 33.9668 Duration 10.3582 SE(Coeff) t-Ratio 1.428 23.8 0.3822 27.1 P-Value <0.0001 <0.0001