Question

1. Suppose that 15 Stata users and 22 Excel users were chosen at random to conduct a series of statistical analyses. The Stata users took 20 minutes on average to complete the tests, with a standard deviation of 5 minutes. The Excel users took 23 minutes on average, with a standard deviation of 10 minutes. Assume test completion time in both cases is normally distributed.
   1. Assume that the standard deviations are known from the population. At the 10% significance level, prove (or fail to prove) that a Stata user will complete the tests faster than an Excel user on average.
      1. Set up the null and alternative hypotheses.
      2. Calculate the appropriate test statistic.
      3. Use either the p-value approach or the critical value approach to reject or fail to reject the null hypothesis.
   2. Assume that the standard deviations are unknown and are sample deviations computed from the respective samples. Repeat question (a) above under this assumption.
   3. Assume that we randomly choose 10 analysts and have each perform the tests using Stata and Excel, with the order in which they do the tests being randomly determined, and obtain a difference mean of 4 and a difference sample standard deviation of 7.5. Repeat step (a) above under this assumption.

Answer 1