\fProblem 1. A pharmaceutical group is running a study to determine if a new dietary aid affects the concentration of adult males shortly after absorbtion. The researchers form two groups that are both independent simple random samples of adult males. The rst group (Group A} is given the new dietary aid and required to complete a puzzlesolving test an hour after taking the aid. The second group (Group B} is given a placebo dietary aid and is also required to complete the same puzzle-solving test an hour after receiving the placebo. The data set \"puzzlegroupsxlsx\" includes the time in minutes to completion for individuals across the two different groups. The researchers are unsure whether the new dietary aid will negatively affect concentration an hour after ingestion or not, so they are only interested in seeing ifthe mean completion time is different between the two groups and not which is faster on average. Construct a hypothesis test at the a = 0.05 signicance level forthis question by completing the steps below. a) State your null and alternative hypothesis. Use ,uA and ,uBto represent the population means for each group. (4.0135) b) State the sample means (in and 3(3), sample standard deviations (5A and 53), and sample sizes (ml and :13} from the data. (6pts) c) Calculate the test statistic. (435) d} State your conclusion with justication (you may either use the p-value or rejection region approach in yourjustication). Use the df= min{nA, H3} - 1 rule we use in class. (4pts) Problem 2. Suppose the following condence interval was derived for a population mean ,u at 90% condence 'om of simple random sample of 25 observations from a Normally distributed population