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

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