Question 3 (20 marks) 3(a) Test whether 2 equals -0.2 against the alternative that 2 is...

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Question 3 (20 marks) 3(a) Test whether 2 equals -0.2 against the alternative that 2 is larger than -0.2 in (1). State the form and sampling distribution of your test statistic under the null, the sample and critical value of your test statistic, your decision rule and your conclusion. (6 marks) 3(b) Derive a model to test the null hypothesis that the birth rate in Eastern states is equal to the birth rate in Northern states, against the alternative hypothesis that the birth rate in the Eastern states is smaller than the birth rate in the Northern states. (5 marks). 3(c) Use the model you derived in part 3(b) to test the null hypothesis specified in 3(b). Test at the 5% significance level. State the null and alternative hypotheses, the form and sampling distribution of your test statistic under the null, the sample and critical value of your test statistic, your decision rule and your conclusion. (6 marks). 3(d) Derive a model to test the null hypothesis that the birth rate in the Southern states is equal to the birth rate in the Eastern and Northern states, against the alternative hypothesis that these birth rates are not all equal. (3 marks) Assume that = E(birth age, north, east, south) Bo+ Biage + Bnorth + Beast + Basouth. state birth age region Alabama 1.63 29.3 South Alaska 2.37 26.1 West Arizona 1.84 29.2 West Arkansas 1.63 30.6 South California 1.7 29.9 West Colorado 1.72 28.6 West Connecti 1.25 32 East Delaware 1.58 29.8 South Florida 1.35 34.7 South Georgia 1.69 28.7 South Hawaii 1.88 28.4 West Idaho 2.14 27.6 West Illinois 1.66 29.9 North Indiana 1.61 29.2 North low a 1.64 30 North Kansas 1.72 30.1 North Kentucky 1.63 29.1 South Louisian 1.95 27.4 South Maine 1.46 30.4 East Maryland 1.42 30.3 South Massach 1.27 31.2 East Michigan 1.57 28.8 North Minnesot 1.66 29.2 North Mississipi 1.9 27.7 South Missouri 1.61 30.9 North Montana 1.81 29 West N. Carolir 1.44 29.6 South N. Dakota 1.84 28.3 North Nebraska 1.74 29.7 North Nevada 1.66 30.2 West New Harr 1.49 30.1 East New Jers 1.32 32.2 East New Mex 2 27.4 West New York 1.36 31.9 East Ohio 1.57 29.9 North Oklahom 1.72 30.1 South Oregon 1.64 30.2 West Pennsylv 1.34 32.1 East Rhode Isl 1.29 31.8 East S. Carolir 1.66 28.1 South S. Dakota 1.92 28.9 North Tenness 1.51 30.1 South Texas 1.92 28.2 South Utah 2.86 24.2 West Vermont 1.54 29.4 East Virginia 1.47 29.8 South W. Virgini 1.51 30.4 South Washing 1.64 29.8 West Wisconsi 1.59 29.4 North Wyoming 2.25 27.1 West Question 3 (20 marks) 3(a) Test whether 2 equals -0.2 against the alternative that 2 is larger than -0.2 in (1). State the form and sampling distribution of your test statistic under the null, the sample and critical value of your test statistic, your decision rule and your conclusion. (6 marks) 3(b) Derive a model to test the null hypothesis that the birth rate in Eastern states is equal to the birth rate in Northern states, against the alternative hypothesis that the birth rate in the Eastern states is smaller than the birth rate in the Northern states. (5 marks). 3(c) Use the model you derived in part 3(b) to test the null hypothesis specified in 3(b). Test at the 5% significance level. State the null and alternative hypotheses, the form and sampling distribution of your test statistic under the null, the sample and critical value of your test statistic, your decision rule and your conclusion. (6 marks). 3(d) Derive a model to test the null hypothesis that the birth rate in the Southern states is equal to the birth rate in the Eastern and Northern states, against the alternative hypothesis that these birth rates are not all equal. (3 marks) Assume that = E(birth age, north, east, south) Bo+ Biage + Bnorth + Beast + Basouth. state birth age region Alabama 1.63 29.3 South Alaska 2.37 26.1 West Arizona 1.84 29.2 West Arkansas 1.63 30.6 South California 1.7 29.9 West Colorado 1.72 28.6 West Connecti 1.25 32 East Delaware 1.58 29.8 South Florida 1.35 34.7 South Georgia 1.69 28.7 South Hawaii 1.88 28.4 West Idaho 2.14 27.6 West Illinois 1.66 29.9 North Indiana 1.61 29.2 North low a 1.64 30 North Kansas 1.72 30.1 North Kentucky 1.63 29.1 South Louisian 1.95 27.4 South Maine 1.46 30.4 East Maryland 1.42 30.3 South Massach 1.27 31.2 East Michigan 1.57 28.8 North Minnesot 1.66 29.2 North Mississipi 1.9 27.7 South Missouri 1.61 30.9 North Montana 1.81 29 West N. Carolir 1.44 29.6 South N. Dakota 1.84 28.3 North Nebraska 1.74 29.7 North Nevada 1.66 30.2 West New Harr 1.49 30.1 East New Jers 1.32 32.2 East New Mex 2 27.4 West New York 1.36 31.9 East Ohio 1.57 29.9 North Oklahom 1.72 30.1 South Oregon 1.64 30.2 West Pennsylv 1.34 32.1 East Rhode Isl 1.29 31.8 East S. Carolir 1.66 28.1 South S. Dakota 1.92 28.9 North Tenness 1.51 30.1 South Texas 1.92 28.2 South Utah 2.86 24.2 West Vermont 1.54 29.4 East Virginia 1.47 29.8 South W. Virgini 1.51 30.4 South Washing 1.64 29.8 West Wisconsi 1.59 29.4 North Wyoming 2.25 27.1 West