Question 1: An engineer wants to compare two different types of steel rods, Rod A and Rod B, for overall fire resistance. She hypothesizes that Rod type A (Group 1) will be better than Rod type B (Group 2), and as such she expects that Rods of type A will be able to withstand higher temperatures before they fail. She plans to get a random sample of rods from both types and put them in a high temperature oven and to record the temperatures at which failure occurs. She expects that the average difference in the measured temperatures between the two group will be about 10 oC. Furthermore, she also assumes that the standard deviation of temperatures for Rods A to be 15 and the standard deviation for rods B to be 17. 

a) The engineers ask you what is the number of rods needed in each group to guarantee an 80% power, assuming equal sized groups. Report the number of rods needed if alpha is 5% and if it is set to 10%. State you Null and alternative hypothesis. b) Now suppose the engineer can only collect data on 60 rods with 30 in each group. What will the statistical power for her t-test be with respect to alpha level of 0.05? c) Try to generate a plot that shows how the sample size (as your y-axis) varies as a function of your Cohens d (as your x-axis) assuming that your power is set to 80% and your alpha is 5%.

 

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