2. A small university is trying to monitor its electricity usage. For a random sample of 30 weekend days (Saturdays and Sundays), the student center used an average of 94.26 kilowatt hours (kWh) with standard deviation 43.29. For a random sample of 60 weekdays, (Monday - Friday), the student center used an average of 112.63 kWh with standard deviation 32.07.(Please show work)

a) Test, at the 5% level, if significantly more electricity is used at the student center, on average, on weekdays than weekend days. Remember to check the conditions, identify the hypotheses, define your parameter, find the test statistic, find the p-value, and give a conclusion in context.

b) Construct a 95% confidence interval for the difference in mean electricity use at the student center between weekdays and weekend days. Use two decimal places in your margin of error.