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 = 0.10.

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      56    38    56    33    38    51    57    55

After       56    38    64    37    43    55    63    61

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