Question

1. According to well-developed national norms, the mean of scores on the OB Anxiety scale among American adults equals 50 and the standard deviation of scores on this inventory equals 15. A researcher wants to assess whether adults living in Canada differ in anxiety from American adults. She has no a priori hypothesis about whether Canadians have higher or lower values (i.e., the key thing of interest at this stage is whether the Canadians simply differ from Americans) She administers the OB scale to 121 randomly sampled Canadian adults. The mean OB score for this sample is 52.5. She assumes that the population standard deviation of Canadian scores is the same as the population standard deviation of American scores.

a. What are her null and alternative hypotheses?

b. Conduct a statistical test of the null hypothesis.

Answer 1

(a)

H0: Null Hypothesis: = 50 ( The adults living in Canada do not differ in anxiety from American adults)

HA: Alternative Hypothesis: 50 ( The adults living in Canada differ in anxiety from American adults) (Claim)

(b)

= 52.5

Hypothesized mean = = 50

= 15

n = 121

Take = 0.05

From Table, critical values of Z = 1.96

Test Statistic is given by:

Since calculated value of Z = 1.833 is less than critical value of Z = 1.96, the difference is not signifcant. Fail to reject null hypothesis.

Coclusion:
The data do not support the claim that the adults living in Canada differ in anxiety from American adults.