A pharmaceutical company wants to market a new drug, but there is a concern that there is an associated side effect of elevated blood pressure. They want to prove that the average increase of the systolic blood pressure number is no more than 5 points. In an experiment with 100 subjects the average elevation of the systolic blood pressure in the sample was 5.4, with sample standard deviation 1.5.

(a) Can you decide at 5% significance level that the population average increase of the systolic blood pressure is above 5 points? Use a one-sided test.

(b) Which error could you possibly have committed in your decision in part (a)?

(c) Calculate the p-value of the above test.

(d) Based on the p-value, what would be your decision at 1% significance level?