Compare the test statistic to the critical value.Determine the critical value by finding the value of the known distribution of the test statistic such that the probability of making a Type I error - which is denoted \(\alpha\) (greek letter "alpha") and is called the " significance level of the test" - is small (typically 0.01, 0.05, or 0.10).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 critical value approach to conducting any hypothesis test are: ![]() ![]() If the test statistic is not as extreme as the critical value, then the null hypothesis is not rejected. That is, it entails comparing the observed test statistic to some cutoff value, called the " critical value." If the test statistic is more extreme than the critical value, then the null hypothesis is rejected in favor of the alternative hypothesis. ![]() The critical value approach involves determining "likely" or "unlikely" by determining whether or not the observed test statistic is more extreme than would be expected if the null hypothesis were true.
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