ESENTIALS OF ECONOMICS STATA Homework 3 Key

Homework 3 Key Directions: Please type in your answer in bold font. For the empirical exercises (where you analyze data using SAS) please attach your SAS code on a separate page of this homework - your SAS code should allow me to replicate the information you used to answer the questions. 1. (Ch.3) Suppose a new standardized test is given to 100 randomly selected third-grade students in New Jersey. The sample average score Y´ on the test is 58 points and the sample standard deviation, SY, is 8 points. a. The authors plan to administer the test to all third-grade students in New Jersey. Construct a 95% confidence interval for the mean score of all New Jersey third graders. Answer: New Jersey sample size 1 n 100, sample average Y1 = 58, and sample standard deviation s1 = 8. The standard error of Y1 is SE( Y1 ) = 1 1 s n / 8/ 100  = 0.8. The 95% confidence interval for the mean score of all New Jersey third graders is 1 1 Y Y             1 96SE( ) 58 1 96 0 8 () This confidence interval indicates that we are 95% confident that the true mean lies between 56.4 and 59.6. b. Suppose the same test is given to 200 randomly selected third graders from Iowa, producing a sample average of 62 points and sample standard deviation of 11 points. Construct a 90% confidence interval for the difference in mean scores between Iowa and New Jersey. Answer: Iowa sample size 2 n  200, sample average Y 2  62, sample standard deviation 2 s 11. The standard error of Y Y 1 2  is SE 2 2 1 2 1 2 64 121 ( ) 1 1158. s s Y Y n n        The 90% confidence interval for the difference in mean score between the two states is 1 2 1 2 ( ) 1 64SE( ) (58 62) ( ) Y Y Y Y                 This confidence interval means that we are 90% confident the actual difference in means between the two states lies between -5.8 and -2.2. Note: the interval doesn’t include 0. c. Can you conclude with a high degree of confidence that the population means for Iowa and New Jersey students are different? (What is the standard error of the difference in the two sample means? What is the p-value of the test of no difference in the means versus some difference?) 1 (Hint: To answer first state the null and alternative hypothesis; second, compute standard error of the difference in the two ample means and then compute the relevant t-statistic; third compute the p-value associated with the t-statistic; and finally use the p-value to answer the question.) Answer: The hypothesis tests for the difference in mean scores is 0 1 2 1 1 2 H H             0 vs 0 From part (b) the standard error of the difference in the two sample means is SE 1 2 ( ) 1 1158. Y Y   The t-statistic for testing the null hypothesis is