Question

(a) A researcher wishes to test the performance of two paper shredders, the Stanley and the Bosch, designed for professional use. Each of 10 randomly selected volunteers shredded 100 sheets of paper with the Stanley, and then another sample of 10 randomly selected volunteers each shredded 100 sheets with the Bosch. The Stanley took an average of 203 seconds to shred 100 sheets with a standard deviation of 6 seconds. The Bosch 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 unequal and unknown standard deviations.

(i) Construct a 99% confidence interval for the difference between the two population means.

(ii) Test whether the claim that mean time taken by the Stanley to shred 100 sheets is higher than that for the Bosch is true, using a 1% significance level.

(iii) Explain what would your decision be in part (b) if the probability of making a Type I error were zero?

Answer 1