The Quantitative Environmental Learning Project (QELP) cited a study by the King County Division of Water and Land Resources on bacteria in various public beaches near Seattle, Washington. For each water sample, bacterial concentrations in colony forming units per 100 milliliters were recorded for two types of bacteria: coliform and E. coli.
a. Was this a paired or two-sample design?
b. Explain why the best summary of spread would not be to report the individual standard deviations.
c. As far as the sample was concerned, which type of bacteria was more common?
d. Produce a histogram of the differences and verify that it is mildly skewed. Does it suggest that there are a few unusually small differences, or a few unusually large differences?
e. The differences in concentrations have mean 81.9 and standard deviation 203.3. To test whether there is evidence that one type of bacteria is more common than the other, first report the standardized sample mean.
f. Tell whether the P-value would be less than 0.05.
g. State your conclusions about whether or not one type of bacteria is more common overall.
h. Use the fact that the t multiplier for 16 degrees of freedom and 95% confidence is 2.12 to produce a confidence interval for the population mean difference.
i. What aspect of your confidence interval in part (h) shows it to be consistent with your conclusion in part (g)?
j. Suppose researchers want to determine whether one type of bacteria tends to increase as the other increases. In this case, does the situation involve one quantitative and one categorical variable, two categorical variables, or two quantitative variables?