10.4 Selecting A Test Statistic
In order to conduct a hypothesis test about a population parameter θ, we need a test statistic (denoted by )—a random variable whose sampling distribution is known under the assumption that the null hypothesis H0: θ = θo is true. Why is a test statistic needed? Because rules pertaining to the rejection or non-rejection of the null hypothesis can be determined for a particular sample outcome by studying the range of values. Specifically, the range of values will be partitioned into the two disjoint or mutually exclusive subsets R and (the complement of R), where,
Next, we need to determine the location and size of the critical region R. In general, the alternative hypothesis H1 determines the location of R while α, the probability of a Type I Error, determines ...
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