Two catalysts are being analyzed to determine how they affec…

Two catalysts are being analyzed to determine how they affect the mean yield of a chemical process. Catalyst 1 is currently used, but catalyst 2 is acceptable.  Since catalyst 2 is cheaper, it should be adopted, providing it does not change the process yield.  An experiment is run in the pilot plant, and 8 batches are made with each catalyst.  Assume that yield is approximately normally distributed and that yield variance is known for each catalyst. Which statistical test should be used to determine whether the mean process yield of catalyst 2 is the same as catalyst 1?

An automobile manufacturer must decide whether to purchase B…

An automobile manufacturer must decide whether to purchase Brand F or Brand M tires for a new car model. To help arrive at a decision, an experiment was conducted using twelve tires of each brand (nF = nM = 12). The tires were tested until tread depth reached 2/32 inches. The average and standard deviation of tire life (in miles) was calculated for both samples. Assume that tire life is approximately normally distributed. Which statistical test should be used to determine whether the two brands have the same variability in tire life?

A project team is tasked with improving the performance of t…

A project team is tasked with improving the performance of the local hockey team.  A literature search returned an article which considered the use of electromyostimulation as a method to train healthy skeletal muscles.  Seventeen players were involved in the study, and the sample standard deviation of performance time during the study was 0.09 seconds. Assume that performance time is approximately normally distributed. Which statistical test should be used to determine whether the standard deviation of performance time is less than the historical value of 0.75 seconds?