2014-03 Test2S.pdf

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Department
Economics for Management Studies
Course
MGEB12H3
Professor
Daga
Semester
Winter

Description
MGEB12H3S – L01, L30, L60 Quantitative Methods in Economics II Test 2 Friday March 21, 2014 3–5 pm Victor Yu Last Name (Print) __Solution____________________ First/Other Names Student Number Time allowed: Two (2) hours Aids allowed: Any Calculator One aid sheet (two 8.5”x11” pages) prepared by student.  This test consists of 22 questions in 12 pages including this cover page.  It is the student’s responsibility to hand in all pages of this test. Any missing page will get zero mark.  Statistical tables (Z, t, Chi Square, F) tables are provided.  Show your work in each question in Part II.  This test is worth 25% of your course grade. Turn to the last page, enter your name and student number again. The University of Toronto's Code of Behaviour on Academic Matters applies to all University of Toronto Scarborough students. The Code prohibits all forms of academic dishonesty including, but not limited to, cheating, plagiarism, and the use of unauthorized aids. Students violating the Code may be subject to penalties up to and including suspension or expulsion from the University. Management, 1265 Military Trail, Toronto, ON, M1C 1A4, Canada 1 www.utsc.utoronto.ca/mgmt Part I. Multiple Choice. 3 marks in each question. No part mark. Circle only one answer. If there are more than one correct answer, circle the best one. 1. Summary statistics computed for two independent samples from two populations are shown as follow: Size Mean Standard Deviation Sample 1 400 305 20 Sample 2 400 300 21 An analyst wishes to test whether the means of two populations are equal or not. The value of the test statistic is closest to (a) 0.45 (b) 1.45 (c) 2.45 √ (d) 3.45 (e) 4.45 Solution: Z  X1 X 2  305 300  3.448 2 2 2 2 S1/n 1 S /2 2 20 /400  21 /400 2. Let y   0  x1 be a regression model with one independent variable, and let  be the correlation between x and y. Which one of the following statements is false? (a) If the F value in the ANOVA table is less than 1, the model is not significant. (b) Testing H :  0 is equivalent to testingH :   0 . 0 1 0 (c) The point estimator b always has the same sign as the sample correlation coefficient r. 1 (d) To test the significance of the model, we must assume that the error  has a normal 2 distribution with mean 0 and variance  . √ (e) The estimated regression equation of y on x is always the same as that of x on y. 3. Let y  0  1  be a regression model with one independent variable. To obtain the sample regression coefficient b1using the method of least squares, which one of the following statements is false? (a) b1 is a random variable and 1 is a constant. n (b)  yi y  0 i1 n   (c)   yi yi  0 i1  n 2 √ (d)  yi y  is a minimum i1 n 2   (e)   yi yi is a minimum i1 2 4. The correlation coefficient from the n pairs of data x1, 1 , x2, y2,..., n , nmay be affected when each x , y is replaced by which of the following? i i (a) xic, y ic  (b) xic, y ic  (c) cxi,cyi, c  0 (d) yi,xi √ (e)  xi, i Questions 5–6, a management recruiter wants to estimate a simple linear regression relationship between X (number of years on a job) and Y (salary in $000) in hotel management. A random sample of 18 observations gives the following summary statistics. Sample Standard Variable Mean Deviation X 5 3 Y 60 5 The sample correlation coefficient is r  0.6. 5. For every year of experience, the expected increase of salary is closest to (a) less than $500 √(b) $1,000 (c) $1,500 (d) $2,000 (e) over $2,000 6. The estimated equation of the regression line is    √(a) Y  55  X (b) Y  5 60X (c) Y  60  5X   (d) Y  5 3X (e) Y  3 5X Questions 7–9. A sample of 17 residential home sales in a city is used to fit a straight-line regression model relating the sale price Y to the square feet of living space X. The resulting least squares  equation is Y  30,000  70X . The standard deviation of X is 100 square feet, and the standard deviation of Y is $8,000. 2 7. The coefficient of determination r is equal to 1 7 49 (a) 0.7 (b) (c) √(d) (e) none of these 8 8 64 8. For a residential home with a living space of 1,000 square feet, the estimated sale price is closest to √(a) $40,000 (b) $70,000 (c) $90,000 (d) $120,000 (e) $150,000 9. Suppose an analyst wishes to create a simple regression model using the same sample data of 17 observations, with X as the dependent variable and Y as the independent variable. The slope of the resulting regression equation is 1 7 7 (a) √(b) (c) (d) 70 (e) none of these 70 640 8 3 Questions 10–11. Two independent random samples are selected to test if alcohol consumption in 1995 is significantly higher than that in 2000. The sample results are summarized below. Sample Consumption (litres) Year Size Average Std Dev 1995 100 18 4 2000 100 16 3 10. To test if alcohol consumption in 1995 is significantly higher than that in 2000, the value of test statistic is closest to (a) 2 √(b) 4 (c) 6 (d) 8 (e) 10 11. At 5% level of significance, the conclusion in question 10 is √(a) Alcohol consumption in 1995 is significantly higher than that in 2000. (b) Alcohol consumption in 1995 is not significantly higher than that in 2000. (c) Alcohol consumption in 1995 does not differ significantly than that in 2000. (d) Alcohol consumption in 1995 differs significantly than that in 2000. (e) none of these Questions 12–13. A company wishes to estimate Sales Volumes (Y in $10,000) from Advertising Expenditure (X in $10,000). A simple regression analysis from a random sample of 10 observations is results the following partial ANOVA table. Source SS df MS F Regression Error 72 Total 1600 The company assumes a positive relationship between Sales Volume and Advertising Expenditure. 12. To test the significance of the model, the value of the t-test is closest to (a) 1.96 √ (b) 3.7712 (c) 14.22 (d) 44.31 (e) 52.14 13. The correlation coefficient between Sales Volume and Advertising Expenditure is equal to (a) 0.49 (b) 0.7 (c) 0.64 √ (d) 0.8 (e) none of these 4 Questions 14–15, a telemarketing company obtains customer names and telephone numbers from two sources. To determine if the percentages of customers who make purchases are the same from both sources, random sample A of size 4000 customers is selected from one source and independently random sample B of size 4000 customers is selected from the other source. Sample A shows that 20% of customers make purchases and sample B shows only a 18%. 14. A 90 percent confidence interval for the difference in the percentages of customers who make purchases is closest to (a) 0.020.0275 (b) 0.0 0.0214 (c) 0.0 0.0195 (d) 0.020.0172 √ (e) 0.0 0.0144 15. To test if the percentages of customers who make purchases are the same from both sources, the p-value is closest to (a) 0.005 (b) 0.0113 √ (c) 0.0226 (d) 0.0312 (e) 0.05 5 Questions 16–17, a market research firm published the following summary statistics for the population of university students regarding their working status in the years of 2001 and 2002. In 2001, 50% of the students worked. In 2002, 52% of the students worked. Among the students who worked, the following population statistics are given: Weekly Income Year Mean Std Dev 2001 $190 $50 2002 $200 $50 16. A random sample of 400 students (no matter they worked or not) is selected from year 2001, and independently a random sample of 400 students (no matter they worked or not) is selected from year 2002. What is the probability that the percent of students working from the sample of 2001 is higher than the percent of students working from the sample in 2002? (a) 0.1 (b) 0.2 √ (c) 0.3 (d) 0.4 (e) 0.5   p1 1  0.5 0.5   0.25  Solution: p1~ N p,1 n   N .5, 400   N .5, 400 ,  1        p2 2   0.52 0.48   0.2496  p2~ N p, 2   N .52,   N .52,   n2   400   400     p q p q   0.250.2496   0.4996  p1 p 2 N p  1 , 2 1 1 2 2   N 0.02,   N 0.02,   n1 n2   400   400          P p 1 p 2  P p 1p 20  P Z   0   0.02  P Z  0.5659  0.2843      0.4996/400  17. A random sample of 100 students is selected from the students who worked in 2001, and independently a random sample of 100 students is selected from the students who worked in 2002. What is the probability that the average weekly income from the sample of 2001 is higher than the average weekly income from the sample in 2002? (a) 0.01 (b) 0.02 (c) 0.04 (d) 0.06 √ (e) 0.08 2 2  50   50  Solution: X 1 N 19, 100  N 190,25 ,X 2 N 20, 100   N 200,25      X 1 X ~2N 10,50 , P X  X  0  P Z  0 10  P Z 1.4142  0.0793 1 2  50 
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