STAT 3450 Lecture Notes - Lecture 16: Statistical Hypothesis Testing, Test Statistic, Sampling Distribution
6 Mar 2017
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Put what you want to prove in the alternative. Make sure the hypotheses refer to the parameters not the statistic. A coating on a rotary gear is supposed to reduce wear below the normal average wear of 80 m. A random sample of 60 gears yielded an average wear of 74 m with a population standard deviation of m 18 . There are two possibilities: the population mean is actually still 80 m with the new coating. The only reason we see a sample mean lower than 80 m is due to sampling variability: the population mean is truly less than 80 m. The lower sample mean is because our initial claim was incorrect. The sample average is less than 80 m, but a statistically significant evidence is needed to make a conclusion that the average wear is less than 80. Find the distribution of the sampling distribution of the statistic assuming the null hypothesis is true.
