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,
is the region of non-rejection: It contains the sample outcomes most favorable to H0.
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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