Setting α, the probability of committing a Type I error, to 0.01, implies that we should reject the null hypothesis when the test statistic Z ≥ 2.3263.
We transform the test statistic Z to the sample mean by way of:
So the observed sample mean is 106.99 or greater.
"=P(Z\\geq{106.9789-110\\over 15\/\\sqrt{ 25}})=P(Z\\geq-1.00703)=0.8430"
In summary, we have determined that we have a 84.30% chance of rejecting the null hypothesis H0: μ = 100 in favor of the alternative hypothesis HA: μ > 100 if the true unknown population mean is in reality μ = 110.
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