PART 1
You are studying the following regression on earnings of a CEO:
Earnings)= 3.86 - 0.28Female + 0.37MarketValue + 0.004Return
You wonder whether any of the independant variables should be introduced in the model in a nonlinear fashion instead. Right now, they are all present in their original form. Which variables must you test to see if a nonlinear version of them is better suited?
A. Earnings, Female, MarketValue, Returns
B. Earnings, MarketValue, Returns
C. Female, MarketValue, Return
D. MarketValue, Returns
PART 2
"A standard ""money demand"" function used by macroeconomists has the form ln(m) = Beta0 + Beta1 ln(GDP) + Beta2 R, Where m is the quantity of (real) money, GDP is the value of (real) gross domestic product, and R is the value of the nominal interest rate measured in percent per year. Supposed that Beta 1 = 1.05 and Beta 2 = -0.03. What is the expected change in m if the interest rate increases from 5% to 9%? Round to nearest integer"
A. decrease 12%
B. decrease 9%
C. increase 12%
D. "decrease $7,387"
PART 3
"This problem is inspired by a study of the ""gender gap"" in earnings in top corporate jobs [Bertrand and Hallock (2001)]. The study compares total compensation among top executives in a large set of U.S. public corporations in the 1990s. (Each year these publicly traded corporations must report total compensation levels for their top five executives.) Let Female be an indicator variable that is equal to 1 for females and 0 for males. A regression of the logarithm of earnings onto Female yields ln(Earnings) = 6.55 -0.41Female, SER = 2.44. The Standard Errors for the Constant is (0.01) and for the Female variable is (0.05). The SER tells us all of the following, except:"
A. The Standard Error of the regression
B. The % of the variance in Earnings we have explained
C. The standard deviation of the regression error
D. The square root of the variance of the residuals
PART 4
"Assume that you had estimated the following quadratic regression model: Test Score = 607.3 + 3.85Income - 0.0423Income2. If income is in thousands, please interpret the coefficient on the Income2 term:"
A. Cannot interpret that coefficient alone
B. A 1 unit increase in income is associated with a 0.0423 points
decrease in TestScores
C. "A $1,000 increase in income is associated with a 0.0423 points
decrease in TestScores"
D. "A $1,000 increase in income is associated with a 4.23 %
decrease in TestScores"
In: Economics
Is the national crime rate really going down? Some sociologists say yes! They say that the reason for the decline in crime rates in the 1980s and 1990s is demographics. It seems that the population is aging, and older people commit fewer crimes. According to the FBI and the Justice Department, 70% of all arrests are of males aged 15 to 34 years†. Suppose you are a sociologist in Rock Springs, Wyoming, and a random sample of police files showed that of 39 arrests last month, 29 were of males aged 15 to 34 years. Use a 5% level of significance to test the claim that the population proportion of such arrests in Rock Springs is different from 70%.
(a) What is the level of significance?
State the null and alternate hypotheses.
H0: p = 0.7;
H1: p ≠ 0.7H0: p
< 0 .7; H1: p =
0.7 H0: p = 0.7;
H1: p > 0.7H0:
p = 0 .7; H1: p <
0.7H0: p ≠ 0.7; H1:
p = 0.7
(b) What sampling distribution will you use?
The Student's t, since np > 5 and
nq > 5.The standard normal, since np > 5 and
nq > 5. The Student's t,
since np < 5 and nq < 5.The standard normal,
since np < 5 and nq < 5.
What is the value of the sample test statistic? (Round
your answer to two decimal places.)
(c) Find the P-value of the test statistic.
(Round your answer to four decimal places.)
Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
At the α = 0.05 level, we reject the null hypothesis
and conclude the data are statistically significant.At the α = 0.05
level, we reject the null hypothesis and conclude the data are not
statistically significant. At the α = 0.05
level, we fail to reject the null hypothesis and conclude the data
are statistically significant.At the α = 0.05 level, we fail to
reject the null hypothesis and conclude the data are not
statistically significant.
(e) Interpret your conclusion in the context of the application.
There is sufficient evidence at the 0.05 level to
conclude that the true proportion of arrests of males aged 15 to 34
in Rock Springs differs from 70%.There is insufficient evidence at
the 0.05 level to conclude that the true proportion of arrests of
males aged 15 to 34 in Rock Springs differs from
70%.
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6. A standard drug is used to treat a certain disease. The probability with which the drug is effective is 0.85. A new drug is developed and it is desired to determine if the new drug performs better than the standard. An experiment was conducted with which 300 people are given the new drug.
a. State symbolically the null and alternative hypotheses.
b. What is the critical value and rejection region of the proposed test?
c. If in fact, the success rate of the drug is 0.9, what is the power of the test?
d. When the experiment was actually carried out, it was found that the new drug was effective in 269 of the patients. Find the p-value of the test.
In: Statistics and Probability