Consider the hummingbird data and information provided in Exercise IV.10.
(a) Do longer wings tend to beat more slowly (i.e., lower frequency) than shorter wings? In plain English, what are the null and alternative hypotheses to be tested?
(b) Compute the value of ts used to test the hypothesis in part (a) for testing HA: p < 0.
(c) Compute the value of ts used to test the hypothesis in part (a) for testing HA: β < 0.
(d) Explain why your answers to (b) and (c) agree.
(e) The P-value for the test of HA: p ≠ 0 is 0.004. Without using a table or computer, what is the P-value for the tests in parts (b) and (c)?