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 that sign that looks like a = 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 51 31 33 44 39 48 40 54
After 46 35 48 50 32 52 59 48