Borrowing money may be necessary for business expansion However, too much borrow

Question

Borrowing money may be necessary for business expansion However, too much borrowed money can also mean trouble. Are developlng 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 Mandbook of International Lconomic Statistics, U.S. Government Documents.) 2 3 4 5 6 7 8 9 10 Country Modern Debt r Cal 94 83 24 89 ta storic Debt per Ca 45 131 86 52 67 32 43 72 Country 11 12 13 14 15 16 17 18 19 20 Modern Debt per Capita L26 24 23 102 75 Historic Deb per Capita L24 13 18 29 109 157 144 117 116 75 Does this information indicate that foreign debt per capita is increasing in developing countries? Use a 0.05 level of significance.

Explanation / Answer

1) Since the countries are same and we are taking data of modern debt and historic debt, we will apply paired t - test here.

The statistical software output for this problem is:

Paired T hypothesis test:
D = 1 - 2 : Mean of the difference between Modern debt per capita and Historic debt per capita
H0 : D = 0
HA : D > 0
Hypothesis test results:

So,

Sample test statistic = 2.29

p - value = 0.0169

2) Statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 29.457998 + 0.95627158 x
Sample size: 10
R (correlation coefficient) = 0.70717873
R-sq = 0.50010175
Estimate of error standard deviation: 3.1510679

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 29.457998 + 0.95627158 x
Sample size: 10
R (correlation coefficient) = 0.70717873
R-sq = 0.50010175
Estimate of error standard deviation: 3.1510679

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

So,

e) For x = 3 job changes, predicted annual salary = 32.33 thousand dollars

f) se = 3.15

g) 90% confidence interval:

Lower limit: 29.73 thousand dollars

Upper limit: 34.93 thousand dollars

h) For slope,

t = 2.829

p - value = 0.0111

Since p - value < 0.05, reject the null hypothesis. Option A is correct.

i) 90% confidence interval:

Lower limit 0.328

Upper limit 1.585

Interpretation: Option B is correct.

Difference Mean Std. Err. DF T-Stat P-value Modern debt per capita - Historic debt per capita 12.7 5.549348 19 2.2885571 0.0169

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