Question

In an exercise in chapter 7, we asked you to conduct a z test to ascertain whether the graded naming test scores for Canadian participants different from the GNT norms based on adults in England. The mean for a sample of 30 adults in Canada was 17.5. The normative mean fro adults in England was 20.4, and we assumed a population standard deviation of 3.2. With 30 participants, the z statistic was -4.97 and we were able to reject the null hypothesis.

a) calculate the test statistic for 3 participants. How does the test statisitc change compared to when N of 30 was used? Conduct step 6 of hypothesis testing. Does your conclusion change? If so, does this meant hat the actual difference between groups changed? Explain.

b) calculate the test statisitc for 100 participants. how does the test statistic change?

c) calculate the test statisitc for 20,000 participants. How does the test statisitic change?

d) what is the effect sample size on the test statisitc?

e) as the test statisitic changes, has the underlying difference between groups changed? Why might this present a problem for hypothesis testing?

Answer 1

(a) The hypothesis being tested is:

H₀: µ = 20.4

H_a: µ ≠ 20.4

The test statistic, z = (x - µ)/σ/√n

z = (17.5 - 20.4)/3.2/√3 = -1.57

The p-value is 0.1165.

Since the p-value (0.1165) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that the graded naming test scores for Canadian participants different from the GNT norms based on adults in England.

(b) z = (17.5 - 20.4)/3.2/√100 = -9.06

The statistic has decreased.

(c) z = (17.5 - 20.4)/3.2/√20000 = -128.16

The statistic has decreased.

(d) As the sample size increases, the test statistic decreases.

(e) The underlying difference between groups has not changed because the difference is independent of the sample size.