The article “Pine Needles as Sensors of Atmospheric Pollution” (Environ. Monitoring, 1982: 273–286) reported on the use of neutron-activity analysis to determine pollutant concentration in pine needles. According to the article’s authors,

“These observations strongly indicated that for those elements which are determined well by the analytical procedures, the distribution of concentration is lognormal. Accordingly, in tests of significance the logarithms of concentrations will be used.” The given data refers to bromine concentration in needles taken from a site near an oil-fired steam plant and from a relatively clean site. The summary values are means and standard deviations of the log-transformed observations.

Let be the true average log concentration at the first site, and define analogously for the second site.

a. Use the pooled t test (based on assuming normality and equal standard deviations) to decide at significance level .05 whether the two concentration distribution means are equal.

b. If and (the standard deviations of the two log concentration distributions) are not equal, would m1 and m2 (the means of the concentration distributions) be the same if ? Explain your reasoning.