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).

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

Fail to reject the null, since the test-statistic value of z is in the critical region defined by the critical value.

Explanation / Answer

Ho: mu = 20.4

H1: mu < 20.4

Statcrunch output of this test is:

One sample Z hypothesis test:
: Mean of population
H0 : = 20.4
HA : < 20.4
Standard deviation = 3.2

Hypothesis test results:

<0.0001

For alpha = 0.05 and left tailed test, critical z - value is - 1.645. So, rejection region is z < -1.645

Calculated z - statistic = -4.9637357

So, reject the null hypothesis.

Option D is correct. Reject the null, since the test - statistic value of z is in the critical region defined by the critical value.

Mean n Sample Mean Std. Err. Z-Stat P-value 30 17.5 0.58423739 -4.9637357

<0.0001

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