A recent study by the World Bank wished to determine whether there was a relationship between the abundance of natural resources in a country and its long term rate of economic growth. Their study used 65 (n) countries over a long period to 1995. Letting Y be the rate of growth measured as a percentage and X be a measure of natural resource abundance, the following relationship between the two variables was estimated. Standard errors of bo and b1 are reported in parentheses under the coefficients for bo and b1
Yhat = 5.358 - 0.0052 X |
(1.380) (0.0030) |
To test the significance of the relationship, a 5% level of significance was adopted.
1. State the direction of the alternative hypothesis used to
test the statistical significance of the relationship. Type gt
(greater than), ge (greater than or equal to), lt (less than), le
(less than or equal to) or ne (not equal to) as appropriate in the
box.
2. Use the tables in the textbook to determine the critical value
(in absolute terms) to three decimal places.
3. Calculate the test statistic, reporting your answer to two
decimal places.
4. Is the null hypothesis rejected for this test? Type yes or
no.
5. Disregarding your answer in part 4, if the null hypothesis was
not rejected, would there appear to be a linear relationship
between resource abundance and economic growth? Type yes or no.
Solution1:
H0:slope=0(no linear realtionship)
Ha:slope=1(linear relationship)
he direction of the alternative hypothesis used to test the statistical significance of the relationship.
ne (not equal to)
Solution2:
2. Use the tables in the textbook to determine the critical value (in absolute terms) to three decimal places.
df=n-2=65-2=63
t crit=T.INV.2T(0.05;63)=1.998
Solution3:
t=slope/std erro of slope=- 0.0052/0.0030=-1.733333
ANSWER:-1.73
Solution4:
4. Is the null hypothesis rejected for this test? Type yes or no
p==T.DIST.2T(1.73;63)
=0.0885
p>0.05
Fail to reject H0.
ANSWER: N0
Solution5:
yes,
if the null hypothesis was not rejected, there appear to be a linear relationship between resource abundance and economic growth
ANSWER:YES
A recent study by the World Bank wished to determine whether there was a relationship between...
A recent study by the World Bank wished to determine whether there was a relationship between the abundance of natural resources in a country and its long term rate of economic growth. Their study used 40 (n) countries over a long period to 1995. Letting Y be the rate of growth measured as a percentage and X be a measure of natural resource abundance, the following relationship between the two variables was estimated. Standard errors of b0 and b1 are...
A recent study by the World Bank wished to determine whether there was a relationship between the abundance of natural resources in a country and its long term rate of economic growth. Their study used 40 (n) countries over a long period to 1995. Letting Y be the rate of growth measured as a percentage and X be a measure of natural resource abundance, the following relationship between the two variables was estimated. Standard errors of b0 and b1 are...
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