Question

Asian economies impact some of the world's largest populations. The growth of an economy has a big influence on the everyday lives of ordinary people. Are Asian economies changing? A random sample of 15 Asian economies gave the following information about annual percentage growth rate. (Reference: Handbook of International Economic Statistics, U.S. Government Documents.)

Region	1	2	3	4	5	6	7	8
Modern Growth Rate %	4.5	2.4	7.4	2.6	0.4	5.4	2.1	4.6
Historic Growth Rate	3.6	1.5	7.5	5.6	3.8	6.5	3.7	8.3

Region	9	10	11	12	13	14	15
Modern Growth Rate %	4.1	5.6	6.9	3.7	3.1	0.1	7.4
Historic Growth Rate	6.9	7.1	6.7	1.2	1.9	2.4	5.4

Does this information indicate a change (either way) in the growth rate of Asian economies? Use a 5% level of significance.

(a) What is the level of significance?

State the null and alternate hypotheses.

1.H_o: Distributions are the same. H₁: Distributions are different.

2.H_o: Distributions are different. H₁: Distributions are the same.    

3.H_o: Distributions are the same. H₁: Distributions are the same.

4.H_o: Distributions are different. H₁: Distributions are different.

(b) Compute the sample test statistic. (Use 2 decimal places.)

What sampling distribution will you use?

1.chi-square

2.Student's t    

3.normal

4.uniform

(c) Find the P-value of the sample test statistic. (Use 4 decimal places.)

(d) Conclude the test?

1.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

2.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.    

3.At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

4.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(e) Interpret your conclusion in the context of the application.

1.Fail to reject the null hypothesis, there is insufficient evidence that the economies are different.

2.Fail to reject the null hypothesis, there is sufficient evidence that the economies are different.    

3.Reject the null hypothesis, there is insufficient evidence that the economies are different.

4.Reject the null hypothesis, there is sufficient evidence that the economies are different.

Answer 1

The statistical software output for this problem is:

Hence,

a) Level of significance = 0.05

Hypotheses: 1.H_o: Distributions are the same. H₁: Distributions are different.

b) Test statistic = -1.50

Student's t

c) P - value = 0.1549

d) 1.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

e) 1.Fail to reject the null hypothesis, there is insufficient evidence that the economies are different.