The measurements of blood pressure on 8 female diabetics are given below. You can assume the distribution is approximately normal.

ID Systolic Diastolic

1 109 73

2 119 80

3 119 74

4 129 82

5 132 90

6 131 100

7 117 95

8 148 100

a)Construct a 95% confidence interval for the mean systolic blood pressure among female diabetics.

b)Test the hypothesis that the mean systolic blood pressure among female diabetics is 130 versus the alternative that the mean is greater than 130.

c)Construct a 95% confidence interval for the difference between mean systolic and diastolic blood pressure among female diabetics.

d)Test the hypothesis that the difference between mean systolic and diastolic blood pressure is 40, with a two-sided alternative.