Question

Problem 1. (10 points) Suppose that from a very large sample you have estimated a parameter beta as 2.80 with estimated variance 0.25. Calculate 90% confidence interval for beta. Problem 2 (15 points) You are working with data in Stata and have a dataset with 935 observations that you would like to use to estimate the returns to education. However, you would like for your sample to be somewhat representative of the general US population in terms of the average IQ which is known to be around 100 in the population. To check this, you perform a test using the variable IQ. Denote by µ its population mean. More specifically, you run a two-sided t-test in Stata and obtain the following output: ttest IQ==100 One-sample t test Variable Obs Mean Std. err. Std. dev. [95% conf. interval] IQ 935 101.2824 .4922738 15.05264 100.3163 102.2484 mean mean (IQ) t H0: mean 100 Degrees of freedom 2.6050 934 Ha: mean < 100 Pr(Tt) 0.9953 Ha: mean! 100 Pr(T> t) = 0.0093 Ha: mean > 100 Pr(T > t) 0.0047 1) What is the null hypothesis being tested in terms of the notation used in class? 2) What is the alternative hypothesis in terms of the notation used in class? 3) Do you reject the null at the 1% significance level (a = 0.01, Ca/2-2.575)? Why or why not? 4) How was the t-statistic t = 2.6050 calculated?

          Problem 1. (10 points)
Suppose that from a very large sample you have estimated a parameter beta as 2.80 with estimated
variance 0.25. Calculate 90% confidence interval for beta.
Problem 2 (15 points)
You are working with data in Stata and have a dataset with 935 observations that you would like
to use to estimate the returns to education. However, you would like for your sample to be
somewhat representative of the general US population in terms of the average IQ which is known
to be around 100 in the population. To check this, you perform a test using the variable IQ. Denote
by µ its population mean. More specifically, you run a two-sided t-test in Stata and obtain the
following output:
ttest IQ==100
One-sample t test
Variable
Obs
Mean Std. err. Std. dev.
[95% conf. interval]
IQ
935
101.2824
.4922738
15.05264
100.3163
102.2484
mean
mean (IQ)
t
H0: mean 100
Degrees of freedom
2.6050
934
Ha: mean < 100
Pr(Tt) 0.9953
Ha: mean! 100
Pr(T> t) = 0.0093
Ha: mean > 100
Pr(T > t)
0.0047
1) What is the null hypothesis being tested in terms of the notation used in class?
2) What is the alternative hypothesis in terms of the notation used in class?
3) Do you reject the null at the 1% significance level (a = 0.01, Ca/2-2.575)? Why or why not?
4) How was the t-statistic t = 2.6050 calculated?

problem 1 10 points suppose that from a very large sample you have estimated a parameter beta as 280 with estimated variance 025 calculate 90 confidence interval for beta problem 2 15 points 84553

Added by Carolyn C.

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