A group of engineers working with physicians in a research hospital is developing a new device to measure blood glucose levels. Based on measurements taken from patients in a previous study, the physicians assert that the new device provides blood glucose levels slightly higher than those provided by the old device. To corroborate their suspicion, 15 diabetic patients were randomly selected, and their blood glucose levels were measured with both the new and the old devices. The measurements, in mg/100 ml, appear in the following table and are stored in the data frame glucose:
(a) Are the samples independent? Why or why not?
(b) If the blood glucose level is a normally distributed random variable, compute a 95% confidence interval for the difference of the population means.
(c) Use the results in (b) to decide whether or not the two devices give the same results.