A sociologist believes that for people under the age of 30, men sleep less hours per night (h/n) on the weekend than women. 59 people were surveyed. Test at alpha =5%. The following summary statistics were determined from the sample. Men Women Mean hrs/n 9.25 10.38 St dev hrs/n 2.95 2.15 n 27 32 a) State the Null and Alternate Hypothesis in symbols and in words. (3pts) b) Calculate the expected results for the hypothesis test sampling distribution, assuming the Null Hypothesis is true. (i.e., name and graph of the sampling distribution, mean and standard error, ASSUME POOLED STANDARD DEVIATIONS) (3pts) c) Identify the standard distribution that best approximates the sampling distribution. (1pts) d) Formulate the decision rule(you can use either critical test scores or p-values) (3pts) e) Determine the statistical sample results, i.e., the differences between the sample means, the pooled standard deviations, the standard error, the test statistic, degrees of freedom and p-value. (16pts) f) Determine the conclusion in terms of the Null and Alternate Hypotheses. Do the sample results indicate that the sociologist's claim is supported at alpha= 5%? (4pts)