Chapter 11.1, Problem 21E

Do certain behaviors result in a severe drain on energy resources because a great deal of energy is expended in comparison to energy intake? The article “The Energetic Cost of Courtship and Aggression in a Plethodontid Salamander” (Ecology [1983]: 979–983) reported on one of the few studies concerned with behavior and energy expenditure. The accompanying table gives oxygen consumption (mL/g/hr) for male-female salamander pairs.

a. The pooled t test is a test procedure for testing H₀: μ₁ – μ₂, = hypothesized value when it is reasonable to assume that the two population distributions are normal with equal standard deviations (σ₁ = σ₂,). The test statistic for the pooled t test is obtained by replacing both s₁ and s₂ in the two-sample t test statistic with s_p where

$s_p=\sqrt{\frac{\left(n_1-1\right)s_1^2+\left(n_2-1\right)s_2^2}{n_1+n_2-2}}$

When the population distributions are normal with equal standard deviations and H₀ is true, the resulting pooled t statistic has a t distribution with df = n₁ + n₂ – 2. For the reported data, the two sample standard deviations are similar. Use the pooled t test with α = 0.05 to determine whether the mean oxygen consumption for courting pairs is higher than the mean oxygen consumption for noncourting pairs.

b. Would the conclusion in Part (a) have been different if the two-sample t test had been used rather than the pooled t test?