Researchers often use z tests to compare their samples to known population norms

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 have 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. Assume the standard deviation of adults in England is 3.2.

If it is hypothesized that Canadians will have a lower mean, the researchers may choose to run a 1-tailed test (alpha = 0.05).

A) For a one-tailed test, choose the appropriate null hypothesis.

Canadian adults have the same average GNT scores as English adults.

B)(step 4) List the appropriate critical value for the 1-tailed test, using the correct sign (negative or positive).

C)What conclusion do you draw from the hypothesis test, and why?

Explanation / Answer

Answers to every thing in detail:

Null hypotheis:

A)
Option D: Canadian adults have the same average GNT scores as English adults.

B)

Sample size = n = 30
Sample Mean = 17.5
Standard deviation = 3.2
Z = (17.5-20.4)/(3.2/sqrt(30)) = -4.96
the critical Z value for one sided alpha=.05 is -1.645

C)

Option B is the right answer
The Z test value of -4.96 is beyond -1.645.
Hence, we reject nul hypothesis, since the test -statistic value of z is in the critical region defined by critical value.

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