In the document "Peak Discharge from Unlogged and Logged Watersheds," J. Jones and G. Grant compiled (paired) data on peak discharge from storms in two watersheds, one unlogged and one logged (100% clear-cut). If there is an effect due to clear-cutting, one would expect that the runoff would be greater in the logged area than in the unlogged area. The runoffs, in cubic meters per second per square kilometer (m3/s/ km2), are provided on the WeissStats CD. Use the technology of your choice to do the following.
a. Formulate the null and alternative hypotheses to reflect the expectation expressed above.
b. Perform the required hypothesis test at the 1% significance level.
c. Obtain and interpret a 99% confidence interval for the difference between mean runoffs in the logged and unlogged watersheds.
d. Construct a histogram of the sample data to identify the approximate shape of the paired-difference variable.
e. Based on your result from part (d), do you think that applying the paired t-procedures in parts (b) and (c) is reasonable? Explain your answer.