Employees of a large corporation are concerned about the declining quality of medical services provided by their group health insurance. A random sample of 100 office visits by employees of this corporation to primary care physicians during 2004 found that the doctors spent an average of 19 minutes with each patient. This year a random sample of 108 such visits showed that doctors spent an average of 15.5 minutes with each patient. Assume that the standard deviations for the two populations are 2.7 and 2.1 minutes, respectively.
a. Construct a 95% confidence interval for the difference between the two population means for these two years.
b. Using a 2.5% level of significance, can you conclude that the mean time spent by doctors with each patient is lower for this year than for 2004?
c. What would your decision be in part b if the probability of making a Type I error were zero? Explain.