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Economic Statistic

Question 1

n=60Zα/2=1.96, from the normal cumulative distribution tables.

ᵐ=$7.22

ᵟ=2.02

Ho:ᵐ=7.22

H1:ᵐ≠7.22

Zstat= (sample mean-ᵐ)/ᵟ/n1/2

Sample mean-7.22=1.96*2.02/601/2

Sample mean=0.5113+7.22

=7.7313.

Question 2

2. a) Ho: Let the population mean wage for the “high” experienced group be X.

H1: Let the population mean wage for the “low” experienced group be Y. such that;

Ho: X=Y=15.9504

H1: X>Y

b) Ttest=14.7697-15.9504/9.257249/1003^1/2

=-4.0393

c) Degrees of freedom=n-1

=1003-1

=1002

d) tα,1002=1.96

e) Hence we fail to reject Ho and conclude that the population mean wage for “high” experienced group is higher than the “low” experienced group.

Question 3

3. a) n=1003

Ho : population variance is the same in the south and the rest of the country.

H1: Population variance in the south is lower than the rest of the country.

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;

b) Ho_X=Y

H1:x<Y

T test=14.7697-14.06619/(9.257249/1003^1/2)

=2.4068

c) Degrees of freedom=(n-1)=1002

d) T(α,1002)=1.96

e) We reject Ho and conclude that the population variance in the south is lower than the rest of the country.

Question 4

a) H0: Return to schooling=10

H1: Return to schooling<10.

b) F test=mean square model/mean square residual

=59.33475447/0.306603416

=193.5228095.

c) F (1,1001)

d) Fail to reject the null hypothesis and conclude that there turn to schooling is 10 percent.

Question 5

5. a.)

i.) UnbiasednessLet’s say an the estimator Ẑ is unbiased estimator of Z if the mean or expectation of Ẑ is equal to the true value Z. That is,

E(Ẑ)=Z for N<∞

ii.) Efficiency

An estimator is said to be efficient if it satisfies two conditions:

Unbiasedness; E(Ẑ)=Z.

Var(Ẑj)≤(Zj)

III.) Consistency

Let Ẑj(n) be an estimator of population parameter Zj on sample size n. Then, zj is a consistent estimator if Ẑj(n) converges in probability to the population parameter zj, such that;

Plim Ẑj(n) =ZjN tends to ∞

b.) Unbiasedness.

This means that on average, the estimator Ẑj 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 Ẑj is centered on the value of Zj, not on other real value.

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).

Work CitedMittelhammer, Ron. Mathematical Statistics for Economics and Business. New York: Springer, 2013. Internet resource.