![]() ![]() Using the known distribution of the test statistic, calculate the P -value: "If the null hypothesis is true, what is the probability that we'd observe a more extreme test statistic in the direction of the alternative hypothesis than we did?" (Note how this question is equivalent to the question answered in criminal trials: "If the defendant is innocent, what is the chance that we'd observe such extreme criminal evidence?").Again, to conduct the hypothesis test for the population mean μ, we use the t-statistic \(t^*=\frac\) which follows a t-distribution with n - 1 degrees of freedom. Using the sample data and assuming the null hypothesis is true, calculate the value of the test statistic. ![]() Specify the null and alternative hypotheses.Specifically, the four steps involved in using the P-value approach to conducting any hypothesis test are: And, if the P-value is greater than \(\alpha\), then the null hypothesis is not rejected. If the P-value is less than (or equal to) \(\alpha\), then the null hypothesis is rejected in favor of the alternative hypothesis. If the P-value is small, say less than (or equal to) \(\alpha\), then it is "unlikely." And, if the P-value is large, say more than \(\alpha\), then it is "likely." The P-value approach involves determining "likely" or "unlikely" by determining the probability - assuming the null hypothesis was true - of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed.
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