Listed below are randomly selected heights (in inches) of males from 1877 and from a recent National Health and Nutrition Examination Survey. Heights from 1877: 71, 64, 68, 70, 70, 69, 67, 67, 68, 68, 67, 66 Heights from 2019: 67, 68, 70, 74, 75, 64, 73, 71, 70, 71, 72, 69 a.) What is the mean and standard deviation of the heights for men in 1877 ? b.) What is the mean and standard deviation of the heights for men in 2019 ? c.) Use a 0.05 significance level to test the claim that heights of men from 1877 have a mean less than men from 2019. Null: The mean height of men from 1877 is the same as the mean height of men from 2019. Alternative: The mean height of men from 1877 is less than the mean height of men from 2019. H_0: H_a: alpha = Test Statistic: t = df = P-value: Conclusion (in a complete sentence): d.) Construct a 95% confidence interval for the mean difference between the heights of men in 1877 compared to men in 2019.