In ongoing economic analyses, the U.S. federal government compares per capita incomes not only among different...

 

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In ongoing economic analyses, the U.S. federal government compares per capita incomes not only among different states but also for the same state at different times. For the 50 states, the sample correlation coefficient relating the 1980 per capita income and the 1999 per capita income is approximately 0.20 (source: U.S. Bureau of Economic Analysis, Survey of Curent Business, May 2000). Based on this information, test for a significant linear relationship between the variables 1980 per capita income and 1999 per capita income by doing a hypothesis test regarding the population correlation coefficient p. (Assume that the two variables have a bivariate normal distribution.) Use the 0.10 level of significance, and perform a two-tailed test. Then fill in the table below. (If necessary, consult a list of formulas.) The null hypothesis: H, :0 The alternative hypothesis: H :0 ロ=ロ The type of test statistic: (Choose one) 口* The value of the test statistic: (Round to at least three decimal places.) The two critical values at the 0.10 level of significance: (Round to at least three decimal places.) I and Based on the data, can we conclude (using the 0.10 level) that there is a significant linear relationship between 1980 per capita income and 1999 per capita income for U.S. states? O Yes O No 口ロ In ongoing economic analyses, the U.S. federal government compares per capita incomes not only among different states but also for the same state at different times. For the 50 states, the sample correlation coefficient relating the 1980 per capita income and the 1999 per capita income is approximately 0.20 (source: U.S. Bureau of Economic Analysis, Survey of Curent Business, May 2000). Based on this information, test for a significant linear relationship between the variables 1980 per capita income and 1999 per capita income by doing a hypothesis test regarding the population correlation coefficient p. (Assume that the two variables have a bivariate normal distribution.) Use the 0.10 level of significance, and perform a two-tailed test. Then fill in the table below. (If necessary, consult a list of formulas.) The null hypothesis: H, :0 The alternative hypothesis: H :0 ロ=ロ The type of test statistic: (Choose one) 口* The value of the test statistic: (Round to at least three decimal places.) The two critical values at the 0.10 level of significance: (Round to at least three decimal places.) I and Based on the data, can we conclude (using the 0.10 level) that there is a significant linear relationship between 1980 per capita income and 1999 per capita income for U.S. states? O Yes O No 口ロ