The z Table
The z table has several uses when the data are distributed normally. If we know an individual raw score, we can convert it to a z statistic and then determine percentages above, below, or at least as extreme as this score. Alternatively, if we know a percentage, we can look up a z statistic on the table and then convert it to a raw score. The table can be used in the same way with means instead of scores.
The Assumptions and Steps of Hypothesis Testing
Assumptions are the criteria that are met, ideally, before a hypothesis test is conducted. Parametric tests are those that require assumptions about the population, whereas nonparametric tests are those that do not. Three basic assumptions apply to many parametric hypothesis tests—
There are six steps that apply to every hypothesis test. First, determine the populations, comparison distribution, and assumptions. This step helps us to choose the appropriate hypothesis test from the diagram in Appendix E, Figure E-1. Second, state the null and research hypotheses. Third, determine the characteristics of the comparison distribution to be used to calculate the test statistic. Fourth, determine the critical values, or cutoffs, usually based on a p level, or alpha, of 0.05, that demarcate the most extreme 5% of the comparison distribution, the critical region. Fifth, calculate the test statistic. Sixth, use that test statistic to decide to reject or fail to reject the null hypothesis. We deem a finding statistically significant when we reject the null hypothesis.
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An Example of the z Test
z tests are conducted in the rare cases in which we have one sample and we know the mean and the standard deviation of the population. We must decide whether to use a one-