The pulse rates below were recorded over a 30-second time period, both before and after a physical fitness regimen. The data is shown below for 8 randomly selected participants. Is there sufficient evidence to conclude that a significant amount of improvement took place? Assume pulse rates are normally distributed.

Test using = 0.05.

· State the null and alternate hypotheses
· find out the mean and standard deviation
· Determine which test statistic applies, and find out it
· Determine the critical value(s).
· State your decision: Should the null hypothesis be rejected?

Before 52 43 31 42 40 48 34 37
After 59 45 58 47 30 48 39 37