Question: 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 a= 0.05.

State the null and alternate hypotheses
Calculate the mean and standard deviation
Determine which test statistic applies, and calculate 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