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.

Question 1- Conduct all six steps of a z test:

STEP 1: Identify the populations,distribution, and assumptions.

STEP 2: State the null and researchhypotheses.

STEP 3: Determine the characteristicsof the comparison distribution.

STEP 4: Determine the critical values,or cutoffs.

STEP 5: Calculate thetest statistic.

STEP 6: Make a decision.

Question 2- When we conduct a one-tailed test instead of atwo-tailed test, there are small changes in steps 2 and 4 ofhypothesis testing. (Note: For this example, assume thatthose from populations other than the one on which it was normedwill score lower, on average. That is, hypothesize that theCanadians will have a lower mean.) Conduct steps 2, 4, and 6 ofhypothesis testing for a one-tailed test.

Question 3- When we change the p level that we use as acutoff, there is a small change in step 4 of hypothesis testing.Although 0.05 is the most commonly used p level, othervalues, such as 0.01, are often used. For this example, conductsteps 4 and 6 of hypothesis testing for a two-tailed test andp level of 0.01, determining the cutoff and drawing thecurve.