Suppose a researcher is studying the effect of a chemical on the concentration of a certain bacteria. She prepares 20 identical bacteria cultures in 20 petri dishes. She randomly assigns each of 5 chemical concentrations (1,2,4,8,16 mg/L) to 4 petri dishes. A bacteria count is obtained for each dish after 24 hours of exposure to the chemical. The researchers notices that the log of the bacteria count seems to be linearly associated with the log of the chemical concentration. The equation of the least-squares regression line for predicting log bacteria count from log chemical concentration is determined to be log(dY ) = 12−1.7 log(X). (Note the least squares regression line gives predictions log(dY ) of log(Y ) on the log scale, and not predictions Yˆ of Y . Also, "log" here refers to the natural log, which is "ln" on your calculator.) The 95% confidence interval for β1 was determined to be -0.2 to -3.2. (a) Fill in the blanks in the following sentence.
A doubling of the chemical concentration was estimated to cause a multiplicative change of (95% confidence interval to ) in the median bacteria count.
(b) Estimate the median bacteria counts for chemical concentrations of 6 and 12 mg/L, respectively. Show that these estimates are consistent with your statement in part a.