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 %	4.7	2.2	7.4	2.6	0.1	5.5	2.2	4.9
Historic Growth Rate	3.4	1.5	7.4	5.8	3.2	6.9	3.3	8.8

Region	9	10	11	12	13	14	15
Modern Growth Rate %	4.2	5.5	6.5	3.7	3.4	0.2	7.6
Historic Growth Rate	6.8	7.4	6.7	1.4	1.5	2.7	5.8

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

Compute the sample test statistic. (Round your answer to two decimal places.)

Find the P-value of the sample test statistic. (Round your answer to four decimal places.)

Borrowing money may be necessary for business expansion. However, too much borrowed money can also mean trouble. Are developing countries tending to borrow more? A random sample of 20 developing countries gave the following information regarding foreign debt per capita (in U.S. dollars, inflation adjusted). (Reference: Handbook of International Economic Statistics, U.S. Government Documents.)

Country	1	2	3	4	5	6	7	8	9	10
Modern Debt per Capita	173	153	123	128	94	84	35	27	27	84
Historic Debt per Capita	145	136	89	113	58	62	36	35	41	73

Country	11	12	13	14	15	16	17	18	19	20
Modern Debt per Capita	24	23	12	27	196	184	142	121	107	79
Historic Debt per Capita	29	11	18	23	105	154	148	119	111	76

Does this information indicate that foreign debt per capita is increasing in developing countries? Use a 0.01 level of significance.

Compute the sample test statistic. (Round your answer to two decimal places.)

Find the P-value of the sample test statistic. (Round your answer to four decimal places.)

Answer 1

1. Let and denote the mean modern and the historic growth rate

To test the hypothesis excel is used.

The output of the test is:

t-Test: Two-Sample Assuming Unequal Variances
	Modern Growth Rate	Historic Growth Rate
Mean	4.046667	4.84
Variance	5.365524	6.288286
Observations	15	15
Hypothesized Mean Difference	0
df	28
t Stat	-0.90005
P(T<=t) one-tail	0.187885
t Critical one-tail	1.701131
P(T<=t) two-tail	0.375769
t Critical two-tail	2.048407

From the output the value of the test statistic is -0.90

p-value = 0.3758

2.  

Let and denote the mean modern and the historic debt rate per capita.

To test the hypothesis excel is used.

The output of the test is:

t-Test: Two-Sample Assuming Unequal Variances
	Modern Debt Rate	Historic Debt Rate
Mean	92.15	79.1
Variance	3547.082	2238.516
Observations	20	20
Hypothesized Mean Difference	0
df	36
t Stat	0.767276
P(T<=t) one-tail	0.22396
t Critical one-tail	2.434494
P(T<=t) two-tail	0.447921
t Critical two-tail	2.719485

From the output the value of the test statistic is 0.77

p-value = (1-0.22396) = 0.776(Since right tail)