A unit of insulin can drop blood glucose level by 50 mg/dl and is used in correcting high blood sugar. The drop of blood sugar level is dependent on an individual’s insulin sensitivities and other circumstances which generally keeps the drop in the range of 15 to 100 mg/dl or more. Ten diabetic patients were randomly selected and their blood sugar levels (in mg/dl)

before and after an insulin therapy was recorded as given in the table below. A hypothesis testing was conducted to determine whether the blood sugar level of diabetic patients after the insulin therapy is less than before the insulin therapy.

Patient # Before After 1 210 211 2 205 199 3 202 205 4 211 202 5 209 194 6 213 217 7 211 198 8 204 163 9 220 178 10 218 222

a) Are the data paired? Explain.

b) Compute the mean difference.

c) Compute the standard deviation of the differences.

d) Compute the standard error of the mean difference.

e) Find the value of the t-statistic.

f) How many degrees of freedom does the t-statistic have?
g) Is the alternative one- or two-sided? Explain.
h) What is the P-value associated with this t-statistic?
(Assume that the other assumptions and conditions for inference are met.)
i) At a = 0.05, what do you conclude?