The Quantitative Environmental Learning Project presents data on widths and lengths of the native butter clam.21 Here is a small random sample of dimensions for four of these clams that we will use to test whether, in general, the clams are longer than they are wide:

a. Use software to carry out a paired t test to see if the mean of differences, width minus length, is negative for the larger population of clams from which the sample was taken: First report the t statistic.

b. Next report the P-value.

c. Is there evidence that the population mean is negative?

d. To see how choice of test procedure can play a role in conclusions, carry out a two-sample t test to see if the difference between population means is negative. (This is not the appropriate procedure because the samples of widths and lengths are not independent, but paired together.) Report the t statistic for this test.

e. Report the P-value.

f. Would the two-sample test provide evidence that the population mean is negative?