Researchers often use z tests to compare their samples to knownpopulation norms. The Graded Naming Test (GNT) asks respondents toname objects in a set of 30 black-and-white drawings. The test,often used to detect brain damage, starts with easy words likekangaroo and gets progressively more difficult, ending with wordslike sextant. The GNT population norm for adults in England is20.4. Roberts (2003) wondered whether a sample of Canadian adultshad different scores than adults in England. If they weredifferent, the English norms would not be valid for use in Canada.The mean for 30 Canadian adults was 17.5. For the purposes of thisexercise, assume that the standard deviation of the adults inEngland is 3.2. Conduct all six steps of a z test. Step one:Identify the populations, Distribution, and assumptions. Step two:State the null and research hypothesis, in both words and symbolicnotation. Step 3:Determine the characteristics of the comparisondistribution. Step four: Determine the critical values, orcutt-offs, indicate the points beyond which we will reject the nullhypothesis. Step five: Calculate the test statistic. Step six:Decide whether to reject or fail to reject the null hypothesis.
