Statistical Inference: A Short Course

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 ...