Please answer 7.6(b) in its entirety, thanks! ing Indicator Variablesmead®iv. State, in terms of the part (b) model parameters, the null hypothesis that the expected mathscore does not differ between boys and girls, against the alternative that there is a difference inexpected math score for boys and girls. What test statistic would you use to carry out this test?What is the distribution of the test statistic assuming the null hypothesis is true, if N = 1200?What is the rejection region for a 5% test?7.7 Can monetary policy reduce the impact of a severe recession? A natural experiment is provided bythe State of Mississippi. In December of 1930, there were a series of bank failures in the southernUnited States. The central portion of Mississippi falls into two Federal Reserve Districts: the sixth(Atlanta Fed) and the eighth (St. Louis Fed). The Atlanta Fed offered "easy money" to banks whilethe St. Louis Fed did not. On July 1, 1930 (just before the crisis), there were 105 State Charter banksin Mississippi in the sixth district and 154 banks in the eighth district. On July 1, 1931 (just afterthe crisis), there were 96 banks remaining in the sixth district and 126 in the eighth district. Thesedata values are from Table 1, Gary Richardson and William Troost (2009) "Monetary InterventionMitigated Banking Panics during the Great Depression: Quasi-Experimental Evidence from a FederalReserve District Border, 1929-1933," Journal of Political Economy, 117(6), 1031-1073.a. Let the eighth district be the control group and the sixth district be the treatment group. Constructa figure similar to Figure 7.3 using the four observations rather than sample means. Identify thetreatment effect on the figure.b. How many banks did each district lose during the crisis? Calculate the magnitude of the treatmenteffect using (7.18) with these four observations, rather than sample means.c. Suppose we have data on these two districts for 1929-1934, so N = 12. Let AFTER, = 1 for yearsafter 1930, and let AFTER, = 0 for years 1929 and 1930. Let TREAT. = 1 for the sixth district and class with a teacher having10 years of experience?iii. What is the null hypothesis, written in terms of the model parameters, that the sex of the childhas no effect on expected math score? What is the alternative hypothesis? What is the teststatistic for the null hypothesis and what is its distribution if the null hypothesis is true? Whatis the test rejection region for a 5% test when N = 1200?iv. It is conjectured that boys may benefit from small classes more than girls. What null and alter-native hypothesis would you test to examine this conjecture? [Hint: Let the conjecture be thealternative hypothesis.]ii. What is the expe7.6 In 1985, the state of Tennessee carried out a statewide experiment with primary school students. Teach-ers and students were randomly assigned to be in a regular-sized class or a small class. The outcomeof interest is a student's score on a math achievement test (MATHSCORE). Let SMALL = 1 if thestudent is in a small class and SMALL = 0 otherwise. The other variable of interest is the number ofyears of teacher experience, TCHEXPER. Let BOY = 1 if the child is male and BOY = 0 if the childis female.a. Write down the econometric specification of the linear regression model explaining MATHSCOREas a function of SMALL, TCHEXPER, BOY and BOY X TCHEXPER, with parameters B₁, B₂,....i. What is the expected math score for a boy in a small class with a teacher having 10 years ofexperience?ii. What is the expected math score for a girl in a regular-sized class with a teacher having10 years of experience?iii. What is the change in the expected math score for a boy in a small class with a teacher having11 years of experience rather than 10?iv. What is the change in the expected math score for a boy in a small class with a teacher having13 years of experience rather than 12?v. State, in terms of the model parameters, the null hypothesis that the marginal effect of teacherexperience on expected math score does not differ between boys and girls, against the alterna-tive that boys benefit more from additional teacher experience. What test statistic would you useto carry out this test? What is the distribution of the test statistic assuming then null hypothesisis true, if N = 1200? What is the rejection region for a 5% test?b. Modify the model in part (a) to include SMALL X BOY.i. What is the expected math score for a boy in a small class with a teacher having 10 years ofexperience?ii. What is the expected math score for a girl in a regular-sized class with a teacher having10 years of experience?iii. What is the expected math score for a boy? What is it for a girl?

Question

Please answer 7.6(b) in its entirety, thanks! ing Indicator Variablesmead®iv. State, in terms of the part (b) model parameters, the null hypothesis that the expected mathscore does not differ between boys and girls, against the alternative that there is a difference inexpected math score for boys and girls. What test statistic would you use to carry out this test?What is the distribution of the test statistic assuming the null hypothesis is true, if N = 1200?What is the rejection region for a 5% test?7.7 Can monetary policy reduce the impact of a severe recession? A natural experiment is provided bythe State of Mississippi. In December of 1930, there were a series of bank failures in the southernUnited States. The central portion of Mississippi falls into two Federal Reserve Districts: the sixth(Atlanta Fed) and the eighth (St. Louis Fed). The Atlanta Fed offered &#34;easy money&#34; to banks whilethe St. Louis Fed did not. On July 1, 1930 (just before the crisis), there were 105 State Charter banksin Mississippi in the sixth district and 154 banks in the eighth district. On July 1, 1931 (just afterthe crisis), there were 96 banks remaining in the sixth district and 126 in the eighth district. Thesedata values are from Table 1, Gary Richardson and William Troost (2009) &#34;Monetary InterventionMitigated Banking Panics during the Great Depression: Quasi-Experimental Evidence from a FederalReserve District Border, 1929-1933,&#34; Journal of Political Economy, 117(6), 1031-1073.a. Let the eighth district be the control group and the sixth district be the treatment group. Constructa figure similar to Figure 7.3 using the four observations rather than sample means. Identify thetreatment effect on the figure.b. How many banks did each district lose during the crisis? Calculate the magnitude of the treatmenteffect using (7.18) with these four observations, rather than sample means.c. Suppose we have data on these two districts for 1929-1934, so N = 12. Let AFTER, = 1 for yearsafter 1930, and let AFTER, = 0 for years 1929 and 1930. Let TREAT. = 1 for the sixth district and class with a teacher having10 years of experience?iii. What is the null hypothesis, written in terms of the model parameters, that the sex of the childhas no effect on expected math score? What is the alternative hypothesis? What is the teststatistic for the null hypothesis and what is its distribution if the null hypothesis is true? Whatis the test rejection region for a 5% test when N = 1200?iv. It is conjectured that boys may benefit from small classes more than girls. What null and alter-native hypothesis would you test to examine this conjecture? [Hint: Let the conjecture be thealternative hypothesis.]ii. What is the expe7.6 In 1985, the state of Tennessee carried out a statewide experiment with primary school students. Teach-ers and students were randomly assigned to be in a regular-sized class or a small class. The outcomeof interest is a student's score on a math achievement test (MATHSCORE). Let SMALL = 1 if thestudent is in a small class and SMALL = 0 otherwise. The other variable of interest is the number ofyears of teacher experience, TCHEXPER. Let BOY = 1 if the child is male and BOY = 0 if the childis female.a. Write down the econometric specification of the linear regression model explaining MATHSCOREas a function of SMALL, TCHEXPER, BOY and BOY X TCHEXPER, with parameters B₁, B₂,....i. What is the expected math score for a boy in a small class with a teacher having 10 years ofexperience?ii. What is the expected math score for a girl in a regular-sized class with a teacher having10 years of experience?iii. What is the change in the expected math score for a boy in a small class with a teacher having11 years of experience rather than 10?iv. What is the change in the expected math score for a boy in a small class with a teacher having13 years of experience rather than 12?v. State, in terms of the model parameters, the null hypothesis that the marginal effect of teacherexperience on expected math score does not differ between boys and girls, against the alterna-tive that boys benefit more from additional teacher experience. What test statistic would you useto carry out this test? What is the distribution of the test statistic assuming then null hypothesisis true, if N = 1200? What is the rejection region for a 5% test?b. Modify the model in part (a) to include SMALL X BOY.i. What is the expected math score for a boy in a small class with a teacher having 10 years ofexperience?ii. What is the expected math score for a girl in a regular-sized class with a teacher having10 years of experience?iii. What is the expected math score for a boy? What is it for a girl?

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