PLEASE ASAP HELP!!!!! - Hypothesis testing

1. (45 marks) Vegetarians who do not supplement their diet with vitamins tend to have elevated homocys teine levels. Elevated homocysteine is associated with early mortality, heart disease, stroke, dementia, and birth defects. In a homocysteine study, the effectiveness of B12 supplement was studied. A simple random sample of 15 vegetarians was selected. Their serum B12 levels were measured before the test. Then they got 50,ug B12 supplement per day. Their serum B12 levels were measured again after three months. The results are recorded in the following table. Before the test 562.8 490.7 489.6 570.5 351.3 464.6 411.0 473.2 545.4 Three months later 685.5 534.7 619.7 699.9 202.7 401.9 336.9 583.4 762.4 Before the test 557.8 428.9 467.0 509.5 479.5 521.1 Three months later 762.4 595.1 580.1 591.5 474.4 589.3 (a) Construct a 99% condence interval for the population mean of the change of the serum B12 levels. (10 marks) (b) Test whether the mean change of the serum B12 levels is greater than 0. (10 marks) (c) Construct a 95% condence interval for the population standard deviation of the change of the serum B12 levels. (10 marks) (d) Test whether more than 60% of the vegetarians' serum B12 levels are improved after getting the B12 supplement? (10 marks) (e) What is the pvalue of the test in (d)