10.6 Types of Hypothesis Tests
The type of test performed will be either a one-tail test (involving either the right or left tail of the sampling distribution of the 
test statistic) or a two-tail test (involving both tails of the same). In general, the type of test reflects the location of R which, as we noted above, is determined by H1.
a. One-tail test (upper tail)
Suppose σ is known. Then our test statistic is 
. (If σ is unknown and thus estimated by s, then we would use the t statistic for small n.) Since H0 is supported by “small values” of 
, R must be located under the right-hand tail of the N(0,1) distribution (H1 “points right”). We thus reject H0 for large values of 
(Fig. 10.1). So if 
> 
(the calculated value of exceeds its tabular value), we fall within the critical region and ...
. (If σ is unknown and thus estimated by s, then we would use the t statistic for small n.) Since H0 is supported by “small values” of , R must be located under the right-hand tail of the N(0,1) distribution (H1 “points right”). We thus reject H0 for large values of (Fig. 10.1). So if > (the calculated value of exceeds its tabular value), we fall within the critical region and ...Get Statistical Inference: A Short Course now with the O’Reilly learning platform.
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