Each of 41 students at a college was asked to calculate their "ecological footprint" -the number of hectares required to support their existence, taking into account such things as the land needed to produce the food they eat and so forth. For 27 women, the average was 6.59, and the standard deviation was 3.89 hectares. For 14 men, the average was 3.96, and the standard deviation was 1.06 hectares.
(a) Use these data to conduct a t test of the null hypothesis that there is no difference between the population means for men and women. Use a two-sided alternative and use α = 0.02. Provide all steps: Construct the value of the test statistic, give bounds on the P-value, and state your conclusion regarding H0.
(b) In nontechnical language, explain to a non statistician what this means about the ecological footprints of men and women at this college. Be specific.
(c) Suppose differences in ecological footprints smaller than 0.7 hectares are considered to be not ecologically important. Compute a confidence interval for the difference in mean global footprint between men and women and discuss whether the difference can be considered "ecologically important."