# Homework 7 ECO 320 – Shorney Construction Company bids

Homework 7ECO 320Due: November 16, 2016, 10PM This assignment is due at the date and time indicated above. Please submit your assignmentelectronically using the Google form HW7 SUBMISSION LINK. Do not forget to check the boxat the bottom of the form to send yourself a copy. Answers to the homework will be posted tothe web at the due time, and no late homeworks will be accepted. If you have any questions orconcerns, 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 workeris 72 or fewer minutes per day. A sample of 30 construction workers will be used to test thisassumption. 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 73minutes?(a) 0.45(b) 0.63(c) 0.88(d) 0.912. Test for the population mean with population variance unknown. The chamber of commerceof a Florida Gulf Coast community advertises that area residential property is available at amean cost of $125,000 or less per lot. Suppose a sample of 32 properties provided a samplemean of $130,000 per lot and a sample standard deviation of $12,500. Use a 0.05 level ofsignificance 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 NationalCenter for Health Statistics showed that the mean age at which women had their first child was25.0 in 2006 (The Wall Street Journal, February 4, 2009). The reporter noted that this was thefirst decrease in the average age at which women had their first child in several years. A recentsample 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 thefirst child. The sample mean is Xdata indicate a change from 2006 in the mean age at which women had their first child? Use1 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 4-5Confidence Intervals for the Sample Mean when the standard deviation ? is known. A samplesurvey 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% confidenceinterval?(a) 2(b) 3(c) 4(d) 55. Develop a 95% confidence interval for the mean price charged by discount brokers for a tradeof 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 6-11The only time you will see a regression calculated by hand is when you are just beginningyour study of econometrics and how ordinary least squares(OLS) works. Regressions arenot normally calculated by hand and that is what computers are for. However seeing how wecalculate 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 EPlease use the following table to answer questions 6-11. 2 ECO 320 FALL 2016 Month DVDEXP INCOME 123456789101112 26.4150.2886.0884.6170.366.4379.1673.0429.57124.99140.97117.62 44036040032068040033650448012641216800 6. Find the ?ˆ1 ?(a) 0.06(b) 0.07(c) 0.08(d) 0.097. Find the ?ˆ0 ?(a) 30.67(b) 35.43(c) 40.12(d) 45.208. Find SST(Total Sum of Squares).(a) 250(b) 13831(c) 7836(d) 469. Find SSE(Explained Sum of Squares).(a) 250(b) 13831(c) 7836(d) 4610. Find SSR(Residual Sum of Squares).(a) 75863 ECO 320 FALL 2016 (b) 13581(c) 204(d) 599611. Find R2 .(a) 0.44(b) 0.56(c) 0.67(d) 0.78Questions 12-15The Coast Starlight Amtrak train that runs from Seattle to Los Angeles. The mean travel timefrom one stop to the next on the Coast Starlight is 129 mins, with a standard deviation of 113minutes. The mean distance traveled from one stop to the next is 108 miles with a standarddeviation of 99 miles. The correlation between travel time and distance is 0.636. You are tryingto predict the travel time with the following model: T RAV ELT IM E = ?0 + ?1 DIST AN CE + u12. Find the ?ˆ1 , which is the best estimator for ?1 .(a) 0.633(b) 0.790(c) 0.817(d) 0.72613. Find the ?ˆ0 , which is the best estimator for ?0(a) 22(b) 35(c) 40(d) 5114. The distance between Santa Barbara and Los Angeles is 103 miles. Use the model to estimatethe time it takes for the Starlight to travel between these two cities.(a) 110(b) 126(c) 130(d) 14515. 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 23384258 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 lot17. Consider the simple linear regression model y = ?0 + ?1 x + u. If E[u] = 0 and x and u areindependent, this implies:(a)(b)(c)(d) E[u|x] = 0x and u are uncorrelatedV ar(u) = 0Both (a) and (b) above are correct 18. If there is a very strong correlation between two variables then the correlation coefficient mustbe(a)(b)(c)(d) any value larger than 1much smaller than 0, if the correlation is negativemuch larger than 0, regardless of whether the correlation is negative or positiveNone of these alternatives is correct. 19. The relationship between number of beers consumed(x) and blood alcohol content(y ) wasstudied in 35 male college students by using least squares regression. The following regression equation was obtained from this study: y = ?0.0127 + 0.0180xThe 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 ythere is evidence that y causes a change in xthere might not be any causal relationship between x and yNone of these alternatives is correct 5