Chapter 11.2, Problem 68E

Preliminary data analyses and other information indicate that you can reasonably assume that, in Exercises 11.63–11.68, the variable under consideration is normally distributed on both populations. For each exercise, use either the critical-value approach or the P-value approach to perform the required hypothesis test.

11.68 Nitrogen and Seagrass. The seagrass Thalassia testudinum is an integral part of the Texas coastal ecosystem. Essential to the growth of T. testudinum is ammonium. Researchers K. Lee and K. Dunton of the Marine Science Institute of the University of Texas at Austin noticed that the seagrass beds in Corpus Christi Bay (CCB) were taller and thicker than those in Lower Laguna Madre (LLM). They compared the sediment ammonium concentrations in the two locations and published their findings in Marine Ecology Progress Series (Vol. 196, pp. 39–48). The summary statistics on sediment ammonium concentrations, in micromoles, obtained by the researchers are shown in the following table.

LLM	CCB
${\bar{x}}_1=24.3$	${\bar{x}}_2=115.1$
s1 = 10.5	s2 = 79.4
n1 = 19	n2 = 51

At the 1% significance level, do the data provide sufficient evidence to conclude that the standard deviation of sediment ammonium concentrations is less in LLM seagrass beds than in CCB seagrass beds? (Note: For df = (50, 18), F_0.01 = 2.78.)