Subject: Economics    / General Economics
Question
Homework 7
ECO 320
Due: November 16, 2016, 10PM This assignment is due at the date and time indicated above. Please submit your assignment
electronically using the Google form HW7 SUBMISSION LINK. Do not forget to check the box
at the bottom of the form to send yourself a copy. Answers to the homework will be posted to
the web at the due time, and no late homeworks will be accepted. If you have any questions or
concerns, please email me at wonho.yeon@stonybrook.edu or TA at yang.yu.2@stonybrook.edu. 1. Shorney Construction Company bids on projects assuming that the mean idle time per worker
is 72 or fewer minutes per day. A sample of 30 construction workers will be used to test this
assumption. Assume that the population standard deviation is 20 minutes. Use ? = 0.05.
What is the probability of making a Type II error when the population mean idle time is 73
minutes?
(a) 0.45
(b) 0.63
(c) 0.88
(d) 0.91
2. Test for the population mean with population variance unknown. The chamber of commerce
of a Florida Gulf Coast community advertises that area residential property is available at a
mean cost of \$125,000 or less per lot. Suppose a sample of 32 properties provided a sample
mean of \$130,000 per lot and a sample standard deviation of \$12,500. Use a 0.05 level of
significance to find the critical value and test the validity of the advertising claim.
(a) 128,745, Accept H0 .
(b) 128,745, Reject H0 .
(c) 132,459, Accept H0 .
(d) 132,459, Accept H0 .
3. Test for the population mean with population variance unknown. Data released by the National
Center for Health Statistics showed that the mean age at which women had their first child was
25.0 in 2006 (The Wall Street Journal, February 4, 2009). The reporter noted that this was the
first decrease in the average age at which women had their first child in several years. A recent
sample of 42 women has been collected concerning the age at which these women had their
¯ = 24.05 and the sample variance is s2 = 34.63. Do the
first child. The sample mean is X
data indicate a change from 2006 in the mean age at which women had their first child? Use
1 ECO 320 FALL 2016 ? = .05.
(a) 24.14, 25.86, Reject H0 .
(b) 24.14, 25.86, Accept H0 .
(c) 23.14, 26.86, Reject H0 .
(d) 23.14, 26.86, Accept H0 .
Questions 4-5
Confidence Intervals for the Sample Mean when the standard deviation ? is known. A sample
survey of 54 discount brokers showed that the mean price charged for a trade of 100 shares at
\$50 per share was \$33.77 (AAII Journal, February 2006). The survey is conducted annually.
With the historical data available, assume a known population standard deviation of \$15.
4. Using the sample data, what is the margin of error(ME) associated with a 95% confidence
interval?
(a) 2
(b) 3
(c) 4
(d) 5
5. Develop a 95% confidence interval for the mean price charged by discount brokers for a trade
of 100 shares at \$50 per share.
(a) [31.77, 35.77]
(b) [30.77, 36.77]
(c) [29.77, 37.77]
(d) [28.77, 38.77]
Questions 6-11
The only time you will see a regression calculated by hand is when you are just beginning
your study of econometrics and how ordinary least squares(OLS) works. Regressions are
not normally calculated by hand and that is what computers are for. However seeing how we
calculate the slope and intercept estimates without a computer will help you understand OLS.
Writing the equation of the regression line for predicting DVD expenditure: DV DEXP = ?ˆ0 + ?ˆ1 IN COM E
Please use the following table to answer questions 6-11. 2 ECO 320 FALL 2016 Month DVDEXP INCOME 1
2
3
4
5
6
7
8
9
10
11
12 26.41
50.28
86.08
84.61
70.3
66.43
79.16
73.04
29.57
124.99
140.97
117.62 440
360
400
320
680
400
336
504
480
1264
1216
800 6. Find the ?ˆ1 ?
(a) 0.06
(b) 0.07
(c) 0.08
(d) 0.09
7. Find the ?ˆ0 ?
(a) 30.67
(b) 35.43
(c) 40.12
(d) 45.20
8. Find SST(Total Sum of Squares).
(a) 250
(b) 13831
(c) 7836
(d) 46
9. Find SSE(Explained Sum of Squares).
(a) 250
(b) 13831
(c) 7836
(d) 46
10. Find SSR(Residual Sum of Squares).
(a) 7586
3 ECO 320 FALL 2016 (b) 13581
(c) 204
(d) 5996
11. Find R2 .
(a) 0.44
(b) 0.56
(c) 0.67
(d) 0.78
Questions 12-15
The Coast Starlight Amtrak train that runs from Seattle to Los Angeles. The mean travel time
from one stop to the next on the Coast Starlight is 129 mins, with a standard deviation of 113
minutes. The mean distance traveled from one stop to the next is 108 miles with a standard
deviation of 99 miles. The correlation between travel time and distance is 0.636. You are trying
to predict the travel time with the following model: T RAV ELT IM E = ?0 + ?1 DIST AN CE + u
12. Find the ?ˆ1 , which is the best estimator for ?1 .
(a) 0.633
(b) 0.790
(c) 0.817
(d) 0.726
13. Find the ?ˆ0 , which is the best estimator for ?0
(a) 22
(b) 35
(c) 40
(d) 51
14. The distance between Santa Barbara and Los Angeles is 103 miles. Use the model to estimate
the time it takes for the Starlight to travel between these two cities.
(a) 110
(b) 126
(c) 130
(d) 145
15. It actually takes the Coast Starlight about 168 mins to travel from Santa Barbara to Los Angeles. Calculate the residual.
4 ECO 320 (a)
(b)
(c)
(d) FALL 2016 23
38
42
58 16. The estimate ?ˆ1 is more likely to be close to its true value ?1 ,
(a) If V ar(?ˆ1 ) is large
(b) If the estimate of the error variance ?ˆ2 is large
(c) If the sample is smaller
(d) If X moves around a lot
17. Consider the simple linear regression model y = ?0 + ?1 x + u. If E[u] = 0 and x and u are
independent, this implies:
(a)
(b)
(c)
(d) E[u|x] = 0
x and u are uncorrelated
V ar(u) = 0
Both (a) and (b) above are correct 18. If there is a very strong correlation between two variables then the correlation coefficient must
be
(a)
(b)
(c)
(d) any value larger than 1
much smaller than 0, if the correlation is negative
much larger than 0, regardless of whether the correlation is negative or positive
None of these alternatives is correct. 19. The relationship between number of beers consumed(x) and blood alcohol content(y ) was
studied in 35 male college students by using least squares regression. The following regression equation was obtained from this study: y = ?0.0127 + 0.0180x
The above equation implies that:
(a)
(b)
(c)
(d) each beer consumed increases blood alcohol by 1.27%
on average it takes 1.8 beers to increase blood alcohol content by 1%
each beer consumed increases blood alcohol by an average of amount of 1.8%
each beer consumed increases blood alcohol by exactly 0.018 20. If two variables, x and y, have a very strong linear relationship, then
(a)
(b)
(c)
(d) there is evidence that x causes a change in y
there is evidence that y causes a change in x
there might not be any causal relationship between x and y
None of these alternatives is correct 5