Question: 6. (25 points) Two random samples of equal size are drawn from firms in Region A and B in Taiwan, n =n2=23. Suppose firms in

6. (25 points) Two random samples of equal size are drawn from firms in Region A and B in Taiwan, n =n2=23. Suppose firms in the two regions follow the Cobb-Douglas production technology with two inputs factors, labor (L) and capital (K). If the model is regressed individually for the two regions. The sums of squared residuals for Region A and B are 340 and 220, respectively. If the firm data from the two regions are pooled together and only one single equation is regressed, the sum of squared residuals is 728. Is it appropriate to pool all the data together and do the empirical study? Conduct a hypothesis test. (a) (5 points) State the corresponding null and alternative hypotheses for the test. (b) (5 points) What is the test statistic used in your hypothesis test? How is the test statistic distributed? (c) (5 points) Can you conclude that firms in the two regions have exactly the same production technology? (d) (5 points) Suppose the regression model is estimated separately for the two regions. E 6. (25 points) Two random samples of equal size are drawn from firms in Region A and B in Taiwan, n =n2=23. Suppose firms in the two regions follow the Cobb-Douglas production technology with two inputs factors, labor (L) and capital (K). If the model is regressed individually for the two regions. The sums of squared residuals for Region A and B are 340 and 220, respectively. If the firm data from the two regions are pooled together and only one single equation is regressed, the sum of squared residuals is 728. Is it appropriate to pool all the data together and do the empirical study? Conduct a hypothesis test. (a) (5 points) State the corresponding null and alternative hypotheses for the test. (b) (5 points) What is the test statistic used in your hypothesis test? How is the test statistic distributed? (c) (5 points) Can you conclude that firms in the two regions have exactly the same production technology? (d) (5 points) Suppose the regression model is estimated separately for the two regions. E

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