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 were true - of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed.
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