A study was conducted to investigate the association between prostate-specific antigen (PSA - a marker for prostate cancer) and acupuncture treatment. Men with elevated PSA levels were recruited from a particular medical clinic. Of the 70 participants recruited, 18 were undergoing regular acupuncture treatments, while 52 were simply monitoring their PSA without undergoing any treatment. Their most recent PSA measurement was recorded (in ng/mL). Assume that PSA measurements are independent. The analyst fit two different one-way ANOVA models to the data. Model 1 used PSA as the response, while Model 2 used log(PSA) - the natural logarithm of PSA - as the response. Some plots and summary statistics are provided below.

For which response - PSA or log(PSA) - do the assumptions of the one-way ANOVA model seem more reasonable? Justify your answer

Construct a 99% confidence interval (CI) for the difference between the mean response of men in the acupuncture group and the mean response of men in the "no treatment" group. Use the response that you selected in (a).

Provide a formal interpretation of your CI in (b).

Using a significance level of 1% and your CI in (b), provide your conclusions regarding the test of whether the mean responses in the two groups differ.

Normal Quantile Plot of Residuals: Response is PSA Summary Statistics for PSA Acupuncture No Treatment Sample mean 3.29 2.67 Sample SD 1.64 1.63 Anddual jogmisNormal Quantile Plot of Residuals: Response is log(PSA) Summary Statistics for log(PSA) Acupuncture No Treatment Sample mean 1.087 0.836 Sample SD 0.457 0.541