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 α = 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 43 34 37 41 41 59 36 58
After 37 36 40 49 52 51 31 55