There were 64 countries in 1992 that competed in the Olympics and won at least one...

  

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There were 64 countries in 1992 that competed in the Olympics and won at least one medal. Let MEDALS be the total number of medals won, and GDP (in billions of 1995 dollars). A linear regression model explaining the number of medals won is MEDALS-B₁ + B₂GDPB + u. The results from estimating the regression are: (standard errors are in parentheses) MEDALS-7.61 +0.013 GDP (s.e) (2.390) (0.002) We want to test the null hypothesis that a one-billion dollar increase in GDP leads to an increase in average number of medals won by 0.015, against the alternative that the effect is less. a). State the null and alternative hypotheses in terms of the model parameters. b) What is the critical t- value for this test using a 5% level of significance? c) What is the critical t- value for this test using a 10% level of significance? d) What is the test statistic for this test? Can you reject the null hypothesis at 10%? at 5%? e) Draw a well labeled diagram for this test (a t-distribution with all the "parts"). Shade in the area that measures the p-value for the test. f) Use R to get an exact measure of the p-value. There were 64 countries in 1992 that competed in the Olympics and won at least one medal. Let MEDALS be the total number of medals won, and GDP (in billions of 1995 dollars). A linear regression model explaining the number of medals won is MEDALS-B₁ + B₂GDPB + u. The results from estimating the regression are: (standard errors are in parentheses) MEDALS-7.61 +0.013 GDP (s.e) (2.390) (0.002) We want to test the null hypothesis that a one-billion dollar increase in GDP leads to an increase in average number of medals won by 0.015, against the alternative that the effect is less. a). State the null and alternative hypotheses in terms of the model parameters. b) What is the critical t- value for this test using a 5% level of significance? c) What is the critical t- value for this test using a 10% level of significance? d) What is the test statistic for this test? Can you reject the null hypothesis at 10%? at 5%? e) Draw a well labeled diagram for this test (a t-distribution with all the "parts"). Shade in the area that measures the p-value for the test. f) Use R to get an exact measure of the p-value.

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a Null Hypothesis B2 0015 Alternative Hypothesis B2 0015 b Critical tValue at 51645 c Critical tVa... View the full answer