Upper-Tail Test

Two-tailed test Upper-tailed test Lower-taded test... 

Once the alternative hypothesis is determined, the nuU hypothesis can be written, which is the opposite of the hypothesis, with the addition of equality. Constructing the null hypothesis after the alternative is often easier for the researcher. If //a is an upper-tail test, such as A is greater than B, then Hj. A > B. The null hypothesis is written as A is equal to or less than B that is, Hq. a < B. If //a is a lower-tail test, then Hq is an upper-tail with an equality ... 

Note that an upper-tail test can be written as a lower-tail test, and a lower-tail test can be written as an upper-tad test simply by reversing the order of the test groups. 

Upper-Tail Test Lower-Tail Test... 

One-tail tests (upper or lower tail) for bi are also possible. If the researcher wants to conduct an upper-tail test (hypothesize that /3i is significantly positive, that is, an ascending regression line), the hypothesis would be... 

FIGURE 2.41 Step 4, decision rule for upper-tail test. 

Using a i-test procedure, this can be done with a slight modification to what we have already done in determining a 1 - a confidence interval for /3o-The two separate /So values can be evaluated as a two-tail test, a lower-tail test, or an upper-tail test. 

Because this is an upper-tail test, the decision rule is... 

If too many runs are present (negative correlation), the same formula is used, but — is used to compensate for an upper-tail test... 

---