AssumeX1Geometric andX2Geometric. Someone has suggested the mean ofX2is exactly 1 unit bigger thanX1but you believe this might be wrong. You sample 31 observations fromX1and get a sample mean of 19 with sample variance of 380. You sample 126 observations ofX2and get a sample mean of 21 with sample variance of 472.

a) Test your belief at the 10% level of significance.

b) Assume you find out the true difference in means is zero (they have the same population mean). Solve for the power of the test you completed in part a)