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Hypothesis testing

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Statistics-prob-value approach and then the traditional approach

1. In a recent year, some professional baseball players complained that umpires were calling more strikes than the average rate of 61.0% called the previous year. At one point in the season, umpire Dan Morrison called strikes in 2231 of 3581 pitches (based on data from USA Today). Use a 0.05 significance level to test the claim that his strike rate is greater than 61.0%.

2. In order to monitor the ecological health of the Florida Everglades, various measurements are recorded at different times. The bottom temperatures are recorded at the Garfield Bight station and the mean of 30.4ºC is obtained for 61 temperatures recorded on 61 different days. Assuming that  = 1.7ºC, test the claim that the population mean is greater than 30.0ºC. Use a 0.05 significance level. (Use classical approach)

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This shows how to use significance level to test hypotheses.

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1. In a recent year, some professional baseball players complained that umpires were calling more strikes than the average rate of 61.0% called the previous year. At one point in the season, umpire Dan Morrison called strikes in 2231 of 3581 pitches (based on data from USA Today). Use a 0.05 significance level to test the claim that his strike rate is greater than 61.0%.

Hypothesis: H0: p = 0.61 vs. HA: p > 0.61
Level of Significance:  = 5%
Decision Rule: Reject the null hypothesis if z > z0.05 = 1.645
or p-value < ...

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