In a study of a super-soldier serum, one issue was the effect of drugs called zeta enablers on the pulse rate of patients during serum injection. The available subjects were divided at random into two groups of 30 patients each. One of the groups received a zeta enabler and the other group received a placebo. The pulse rate of each patient at time of serum injection was recorded. The treatment group had a mean pulse rate of 65.2 and a standard deviation of 7.8. For the control group, the mean pulse rate was 70.3 and the standard deviation was 8.3.

1. Find the standard error for the difference in mean pulse rates between the two groups.
2. Construct and interpret a 99% confidence interval for the difference in mean pulse rates.
3. Suppose we want to test the hypothesis that zeta enablers reduce mean pulse rate. State the null and alternative hypotheses for this test.
4. The test statistic is t= - 2.453. Determine the p-value and draw the appropriate conclusion using =0.05.