Your Name <\/p>\n
Instructor <\/p>\n
Subject<\/p>\n
Date of submission<\/p>\n
Economic Statistic<\/p>\n
Question 1<\/p>\n
n=60Z\u03b1\/2=1.96, from the normal cumulative distribution tables.<\/p>\n
\u1d50=$7.22<\/p>\n
\u1d5f=2.02<\/p>\n
Ho:\u1d50=7.22<\/p>\n
H1:\u1d50\u22607.22<\/p>\n
Zstat= (sample mean-\u1d50)\/\u1d5f\/n1\/2<\/p>\n
Sample mean-7.22=1.96*2.02\/601\/2<\/p>\n
Sample mean=0.5113+7.22<\/p>\n
=7.7313.<\/p>\n
Question 2<\/p>\n
2. a) Ho: Let the population mean wage for the \u201chigh\u201d experienced group be X.<\/p>\n
H1: Let the population mean wage for the \u201clow\u201d experienced group be Y. such that;<\/p>\n
Ho: X=Y=15.9504<\/p>\n
H1: X>Y<\/p>\n
b) Ttest=14.7697-15.9504\/9.257249\/1003^1\/2<\/p>\n
=-4.0393<\/p>\n
c) Degrees of freedom=n-1<\/p>\n
=1003-1<\/p>\n
=1002<\/p>\n
d) t\u03b1,1002=1.96<\/p>\n
e) Hence we fail to reject Ho and conclude that the population mean wage for \u201chigh\u201d experienced group is higher than the \u201clow\u201d experienced group.<\/p>\n
Question 3<\/p>\n
3. a) n=1003<\/p>\n
Ho : population variance is the same in the south and the rest of the country.<\/p>\n
H1: Population variance in the south is lower than the rest of the country.<\/p>\n
Let population variance from the south be X and the population variance from the rest of the country be Y, so that the hypothesis becomes;<\/p>\n
b) Ho_X=Y<\/p>\n
H1:x<Y<\/p>\n
T test=14.7697-14.06619\/(9.257249\/1003^1\/2)<\/p>\n
=2.4068<\/p>\n
c) Degrees of freedom=(n-1)=1002<\/p>\n
d) T(\u03b1,1002)=1.96<\/p>\n
e) We reject Ho and conclude that the population variance in the south is lower than the rest of the country.<\/p>\n
Question 4<\/p>\n
a) H0: Return to schooling=10<\/p>\n
H1: Return to schooling<10.<\/p>\n
b) F test=mean square model\/mean square residual<\/p>\n
=59.33475447\/0.306603416<\/p>\n
=193.5228095.<\/p>\n
c) F (1,1001)<\/p>\n
d) Fail to reject the null hypothesis and conclude that there turn to schooling is 10 percent.<\/p>\n
Question 5<\/p>\n
5. a.) <\/p>\n
i.) UnbiasednessLet\u2019s say an the estimator \u1e90 is unbiased estimator of Z if the mean or expectation of \u1e90 is equal to the true value Z. That is,<\/p>\n
E(\u1e90)=Z for N<\u221e<\/p>\n
ii.) Efficiency<\/p>\n
An estimator is said to be efficient if it satisfies two conditions:<\/p>\n
Unbiasedness; E(\u1e90)=Z.<\/p>\n
Var(\u1e90j)\u2264(Zj)<\/p>\n
III.) Consistency<\/p>\n
Let \u1e90j(n) be an estimator of population parameter Zj on sample size n. Then, zj is a consistent estimator if \u1e90j(n) converges in probability to the population parameter zj, such that;<\/p>\n
Plim \u1e90j(n) =ZjN tends to \u221e <\/p>\n
b.) Unbiasedness.<\/p>\n
This means that on average, the estimator \u1e90j is correct even though any single estimator of Zj for a specific given sample data may not be equal to Zj. The finite sample distribution of the estimator \u1e90j is centered on the value of Zj, not on other real value.<\/p>\n
c.) Variance of an estimator is an inverse of statistical spread or dispersion around the mean, such that smaller variance indicates more statistical precision. Thus, minimum variance is, therefore, statistical for most precise estimator of an unknown population parameter .d.) Cov(Y, X) =E (YX)-E(Y) E(x).<\/p>\n
Work CitedMittelhammer, Ron. Mathematical Statistics for Economics and Business. New York: Springer, 2013. Internet resource.<\/p>\n","protected":false},"excerpt":{"rendered":"
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