Five pairs of tests are conducted to compare two methods of making rope. Each sample batch contains enough hemp to make two ropes. The tensile strength measurements are
(a) Treat the data as 5 paired observations and calculate a 95% confidence interval for the mean difference in tensile strengths between ropes made by the two methods.
(b) Repeat the calculation of a 95% confidence interval treating the data as independent random samples.
(c) Briefly discuss the conditions under which each type of analysis would be appropriate.