A consumer organization tested two paper shredders, the Piranha and the Crocodile, designed for home use. Each of 10 randomly selected volunteers shredded 100 sheets of paper with the Piranha, and then another sample of 10 randomly selected volunteers each shredded 100 sheets with the Crocodile. The Piranha took an average of 203 seconds to shred 100 sheets with a standard deviation of 6 seconds. The Crocodile took an average of 187 seconds to shred 100 sheets with a standard deviation of 5 seconds. Assume that the shredding times for both machines are normally distributed with equal but unknown standard deviations.
a. Construct a 99% confidence interval for the difference between the two population means.
b. Using a 1% significance level, can you conclude that the mean time taken by the Piranha to shred 100 sheets is higher than that for the Crocodile?
c. What would your decision be in part b if the probability of making a Type I error were zero? Explain.