The accompanying data on food intake (in kcal) for 15 men on the day following two nights of only 4 hours of sleep each night and for 15 men on the day following two nights of 8 hours of sleep each night is consistent with summary quantities in the paper "short-term sleep loss decreases physical activity under free-living conditions but does not increase food intake under time deprived laboratory conditions in healthy men" (american journal of clinical nutrition [2009]: 1476–1482). the men participating in this experiment were randomly assigned to one of the two sleep conditions. 4-hour sleep group: 3585 4470 3068 5338 2221 4791 4435 3099 3187 3901 3868 3869 4878 3632 4518 8-hour sleep group: 4965 3918 1987 4993 5220 3653 3510 3338 4100 5792 4547 3319 3336 4304 4057 verify the assumption of approximate normality for each of the populations. carry out a two-sample t test with α = 0.05 to determine if there is a significant difference in mean food intake for the two different sleep conditions. (use a statistical computer package to calculate the p-value. use μ4-hour − μ8-hour. round your test statistic to two decimal places, your df down to the nearest whole number, and your p-value to three decimal places.)