Question

Researchers often use z tests to compare their samples to known population norms. The Graded Naming Test (GNT) asks respondents to name objects in a set of 30 black-and-white drawings. The test, often used to detect brain damage, starts with easy words like kangaroo and gets progressively more difficult, ending with words like sextant. The GNT population norm for adults in England is 20.4. Roberts (2003) wondered whether a sample of Canadian adults had different scores than adults in England. If they were different, the English norms would not be valid for use in Canada. The mean for 30 Canadian adults was 17.5. For the purposes of this exercise, assume that the standard deviation of the adults in England 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 research hypotheses.

STEP 3: Determine the characteristics of the comparison distribution.

STEP 4: Determine the critical values, or cutoffs.

STEP 5: Calculate the test statistic.

STEP 6: Make a decision.

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

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

Answer 1