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ECON 216 BUSINESS STATISTICS MCLA NAME: __________________STUDENT ID: _______ EXAM 1_ PART II_50 Points Organizing and Visualizing Data TABLE 1 An insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for automobile insurance. A representative from a local insurance agency selected a random sample of insured drivers and recorded, X, the number of claims each made in the last 3 years, with the following results. X 1 2 3 4 5 f 14 18 12 5 1 1) Referring to Table 1, how many drivers are represented in the sample? 2) Referring to Table 1, how many total claims are represented in the sample? 3) A type of vertical bar chart in which the categories are plotted in the descending rank order of the magnitude of their frequencies is called a TABLE 2 Every spring semester, the School of Business coordinates a luncheon with local business leaders for graduating seniors, their families, and friends. Corporate sponsorship pays for the lunches of each of the seniors, but students have to purchase tickets to cover the cost of lunches served to guests they bring with them. The following histogram represents the attendance at the senior luncheon, where X is the number of guests each graduating senior invited to the luncheon and f is the number of graduating seniors in each category. 4) Referring to the histogram from Table 2, how many graduating seniors attended the luncheon? 5) A professor of economics at a small Texas university wanted to determine what year in school students were taking his tough economics course. Shown below is a pie chart of the results. What percentage of the class took the course prior to reaching their senior year? Numerical Descriptive Measures Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid. The ages of 25 senior citizens were as follows: TABLE 3: 60 61 62 63 64 65 66 68 68 69 70 73 73 74 75 76 76 81 81 82 86 87 89 90 92 6) Referring to Table 3, calculate the arithmetic Mean, Median, and Mode age of the senior citizens to the nearest hundredth of a year. 7) The prices of Hamburgers and Fish burgers at MCLA on menu are posted as follow: X: Hamburgers Price $ 8, $ 6, $ 4 Y: Fish Burgers Price $ 7, $ 5, $ 3 Compute the Mean, Standard Deviation, and Coefficient of Variation for Hamburgers and Fish Burgers. PROBABILITY 2/6/2014 5:18:00 PM Chapter 4 Basic Probability 66) A business venture can result in the following outcomes (with their corresponding chance of occurring in parentheses): Highly Successful (10%), Successful (25%), Break Even (25%), Disappointing (20%), and Highly Disappointing (?). If these are the only outcomes possible for the business venture, what is the chance that the business venture will be considered Highly Disappointing? A) 10% B) 15% C) 20% D) 25% Answer: C Difficulty: Easy Keywords: marginal probability 67) A survey of banks revealed the following distribution for the interest rate being charged on a home loan (based on a 30-year mortgage with a 10% down payment). Interest Rate 3.20% to 3.29% 3.30% to 3.39% 3.40% to 3.49% 3.50% to 3.59% 3.60% and above Probability 0.12 0.23 0.24 0.35 0.06 If a bank is selected at random from this distribution, what is the chance that the interest rate charged on a home loan will exceed 3.49%? A) 0.06 B) 0.41 C) 0.59 D) 1.00 Answer: B Difficulty: Easy Keywords: marginal probability, addition rule TABLE 4-1 Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasized the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below: 68) Referring to Table 4-1, what proportion of accidents involved more than one vehicle? A) 50/400 or 12.5% B) 75/400 or 18.75% C) 275/400 or 68.75% D) 325/400 or 81.25% Answer: D Difficulty: Easy Keywords: contingency table, empirical classical probability, addition rule 69) Referring to Table 4-1, what proportion of accidents involved alcohol and a single vehicle? A) 25/400 or 6.25% B) 50/400 or 12.5% C) 195/400 or 48.75% D) 245/400 or 61.25% Answer: B Difficulty: Easy Keywords: contingency table, empirical classical probability, joint probability 70) Referring to Table 4-1, what proportion of accidents involved alcohol or a single vehicle? A) 25/400 or 6.25% B) 50/400 or 12.5% C) 195/400 or 48.75% D) 245/400 or 61.25% Answer: C Difficulty: Easy Keywords: contingency table, empirical classical probability, addition rule 71) Referring to Table 4-1, given alcohol was involved, what proportion of accidents involved a single vehicle? A) 50/75 or 66.67% B) 50/170 or 29.41% C) 120/170 or 70.59% D) 120/400 or 30% Answer: B Difficulty: Easy Keywords: contingency table, empirical classical probability, marginal probability 72) Referring to Table 4-1, given that multiple vehicles were involved, what proportion of accidents involved alcohol? A) 120/170 or 70.59% B) 120/230 or 52.17% C) 120/325 or 36.92% D) 120/400 or 30% Answer: C Difficulty: Easy Keywords: contingency table, empirical classical probability, conditional probability, addition rule Probability Counting Rules 73) A new model car from Ford Motor Company offers a keyless entry system that utilizes a four-letter code. How many different possible combinations are there for the code? Answer: 456,976 Difficulty: Easy Keywords: counting rule 74) There are 10 finalists at a national dog show. How many different orders of finishing can there be for all the 10 finalists? Answer: 3,628,800 Difficulty: Easy Keywords: counting rule, permutation 75) There are only 4 empty rooms available in a student dormitory for eleven new freshmen. Each room is considered unique so that it matters who is being assigned to which room. How many different ways can those 4 empty rooms be filled, one student per room? Answer: 7,920 Difficulty: Easy Keywords: counting rule, permutation Chapter 5 Discrete Probability Distributions 76) If n = 10 and π = 0.70, then the mean of the binomial distribution is A) 0.07. B) 1.45. C) 7.00. D) 14.29. Answer: C Difficulty: Easy Keywords: binomial distribution, mean 77) If n = 10 and π = 0.70, then the standard deviation of the binomial distribution is A) 0.07. B) 1.45. C) 7.00. D) 14.29. Answer: B Difficulty: Easy Keywords: binomial distribution, standard deviation TABLE 5-4 The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Corvallis, Oregon. X 0 1 2 3 4 5 P(X) 0.10 0.20 0.45 0.15 0.05 0.05 78) Referring to Table 5-4, the mean or expected value of the number of accidents is ________. Answer: 2.0 Difficulty: Easy Keywords: probability distribution, mean REGRESSION ANALYSIS 2/6/2014 5:18:00 PM Chapter 13 Simple Linear Regression 1) The Y-intercept (b0) represents the A) predicted value of Y when X = 0. B) change in estimated Y per unit change in X. C) predicted value of Y. D) variation around the sample regression line. Answer: A Difficulty: Easy Keywords: intercept, interpretation 2) The Y-intercept (b0) represents the A) estimated average Y when X = 0. B) change in estimated average Y per unit change in X. C) predicted value of Y. D) variation around the sample regression line. Answer: A Difficulty: Easy Keywords: intercept, interpretation 3) The slope (b1) represents A) predicted value of Y when X = 0. B) the estimated average change in Y per unit change in X. C) the predicted value of Y. D) variation around the line of regression. Answer: B Difficulty: Easy Keywords: slope, interpretation 4) The least squares method minimizes which of the following? A) SSR B) SSE C) SST D) All of the above. Answer: B Difficulty: Difficult Keywords: least squares, properties TABLE 13-1 A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank's charges (Y)—measured in dollars per month—for services rendered to local companies. One independent variable used to predict service charges to a company is the company's sales revenue (X)— measured in millions of dollars. Data for 21 companies who use the bank's services were used to fit the model: Yi = β0 + β1Xi + εi The results of the simple linear regression are provided below. 5) Referring to Table 13-1, interpret the estimate of β0, the Y-intercept of the line. A) All companies will be charged at least $2,700 by the bank. B) There is no practical interpretation since a sales revenue of $0 is a nonsensical value. C) About 95% of the observed service charges fall within $2,700 of the least squares line. D) For every $1 million increase in sales revenue, we expect a service charge to decrease $2,700. Answer: B Difficulty: Moderate Keywords: intercept, interpretation 6) Referring to Table 13-1, interpret the estimate of σ, the standard deviation of the random error term (standard error of the estimate) in the model. A) About 95% of the observed service charges fall within $65 of the least squares line. B) About 95% of the observed service charges equal their corresponding predicted values. C) About 95% of the observed service charges fall within $130 of the least squares line. D) For every $1 million increase in sales revenue, we expect a service charge to increase $65. Answer: C Difficulty: Difficult Keywords: standard error of estimate, interpretation 7) Referring to Table 13-1, interpret the p-value for testing whether β1exceeds 0. A) There is sufficient evidence (at the α = 0.05) to conclude that sales revenue (X) is a useful linear predictor of service charge (Y). B) There is insufficient evidence (at the α = 0.10) to conclude that sales revenue (X) is a useful linear predictor of service charge (Y). C) Sales revenue (X) is a poor predictor of service charge (Y). D) For every $1 million increase in sales revenue, you expect a service charge to increase $0.034. Answer: A Difficulty: Moderate Keywords: p-value, interpretation 8) Referring to Table 13-1, a 95% confidence interval for β1 is (15, 30). Interpret the interval. A) You are 95% confident that the mean service charge will fall between $15 and $30 per month. B) You are 95% confident that the sales revenue (X) will increase between $15 and $30 million for every $1 increase in service charge (Y). C) You are 95% confident that mean service charge (Y) will increase between $15 and $30 for every $1 million increase in sales revenue (X). D) At the α = 0.05 level, there is no evidence of a linear relationship between service charge (Y) and sales revenue (X). Answer: C Difficulty: Moderate Keywords: confidence interval, interpretation TABLE 13-2 A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below: City Price ($) Sales River City 1.30 100 Hudson 1.60 90 Ellswort 1.80 h 90 Prescott 2.00 40 Rock Elm 2.40 38 Stillwate 2.90 r 32 9) Referring to Table 13-2, what is the estimated slope for the candy bar price and sales data? A) 161.386 B) 0.784 C) -3.810 D) -48.193 Answer: D Difficulty: Moderate Keywords: slope, estimation 10) Referring to Table 13-2, what is the estimated mean change in the sales of the candy bar if price goes up by $1.00? A) 161.386 B) 0.784 C) -3.810 D) -48.193 Answer: D Difficulty: Moderate Keywords: slope, interpretation 11) Referring to Table 13-2, what is the coefficient of correlation for these data? A) -0.8854 B) -0.7839 C) 0.7839 D) 0.8854 Answer: A Difficulty: Moderate Keywords: coefficient of correlation, estimation 12) Referring to Table 13-2, what is the percentage of the total variation in candy bar sales explained by the regression model? A) 100% B) 88.54% C) 78.39% D) 48.19% Answer: C Difficulty: Moderate Keywords: coefficient of determination, interpretation 13) Referring to Table 13-2, what percentage of the total variation in candy bar sales is explained by prices? A) 100% B) 88.54% C) 78.39% D) 48.19% Answer: C Difficulty: Moderate Keywords: coefficient of determination, interpretation 14) Referring to Table 13-2, what is the standard error of the estimate, SYX, for the data? A) 0.784 B) 0.885 C) 12.650 D) 16.299 Answer: D Difficulty: Moderate Keywords: standard error of estimate, estimation 15) Referring to Table 13-2, what is the standard error of the regression slope estimate, ? A) 0.784 B) 0.885 C) 12.650 D) 16.299 Answer: C Difficulty: Moderate Keywords: standard error, slope 16) Referring to Table 13-2, what is for these data? A) 0 B) 1.66 C) 2.54 D) 25.66 Answer: B Difficulty: Moderate Keywords: sum of squares 17) Referring to Table 13-2, to test that the regression coefficient, β1, is not equal to 0, what would be the critical values? Use α = 0.05. A) ±2.5706 B) ±2.7764 C) ±3.1634 D) ±3.4954 Answer: B Difficulty: Difficult Keywords: t test on slope, critical value 18) Referring to Table 13-2, to test whether a change in price will have any impact on sales, what would be the critical values? Use α = 0.05. A) ±2.5706 B) ±2.7765 C) ±3.1634 D) ±3.4954 Answer: B Difficulty: Difficult Keywords: t test on slope, critical value 19) Referring to Table 13-2, if the price of the candy bar is set at $2, the estimated mean sales will be A) 30. B) 65. C) 90. D) 100. Answer: B Difficulty: Moderate Keywords: estimation of mean values 20) Referring to Table 13-2, if the price of the candy bar is set at $2, the predicted sales will be A) 30. B) 65. C) 90. D) 100. Answer: B Difficulty: Moderate Keywords: prediction of individual values dard error of estimate, interpretation EXTRA CREDIT: Chapter 14 Introduction to Multiple Regression TABLE 14-10 21) You worked as an intern at We Always Win Car Insurance Company last summer. You notice that individual car insurance premiums depend very much on the age of the individual and the number of traffic tickets received by the individual. You performed a regression analysis in EXCEL and obtained the following partial information: 22) Referring to Table 14-10, the proportion of the total variability in insurance premiums that can be explained by AGE and TICKETS is ________. Answer: 0.7303 Difficulty: Easy Keywords: coefficient of multiple determination, interpretation 23) Referring to Table 14-10, the proportion of the total variability in insurance premiums that can be explained by AGE and TICKETS after adjusting for the number of observations and the number independent variables is ________. Answer: 0.6853 Difficulty: Easy Keywords: adjusted r-square 24) Referring to Table 14-10, the standard error of the estimate is ________. Answer: 226.7502 Difficulty: Easy Keywords: standard error of estimate 25) Referring to Table 14-10, the estimated mean change in insurance premiums for every 2 additional tickets received is ________. Answer: (243.4401)∗2 = 486.8802 Difficulty: Difficult Keywords: slope, interpretation 26) Referring to Table 14-10, the 99% confidence interval for the change in mean insurance premiums of a person who has become 1 year older (i.e., the slope coefficient for AGE) is -1.4061 ± ________. Answer: 7.9382 Difficulty: Moderate Keywords: slope, interpretation, confidence interval 27) Referring to Table 14-10, the total degrees of freedom that are missing in the ANOVA table should be ________. Answer: 14 Difficulty: Easy Keywords: degrees of freedom 28) Referring to Table 14-10, the regression sum of squares that is missing in the ANOVA table should be ________. Answer: 1,670,569.3000 Difficulty: Easy Keywords: sum of squares 29) Referring to Table 14-10, the residual mean squares (MSE) that are missing in the ANOVA table should be ________. Answer: 51,415.6517 Difficulty: Easy Keywords: mean squares 30) Referring to Table 14-10, to test the significance of the multiple regression model, what is the form of the null hypothesis? A) H0 : β1 = 0 B) H0 : β2= 0 C) H0 : β1 = β2 = 0 D) H0 : β0 = β1 = β2 = 0 Answer: C Difficulty: Easy Keywords: F test on the entire regression, form of hypothesis 31) Referring to Table 14-10, to test the significance of the multiple regression model, the value of the test statistic is ________. Answer: 16.2457 Difficulty: Easy Keywords: F test on the entire regression, test statistic 32) Referring to Table 14-10, to test the significance of the multiple regression model, the p-value of the test statistic in the sample is ________. Answer: 0.0004 Difficulty: Easy Keywords: F test on the entire regression, p-value 33) To explain personal consumption (CONS) measured in dollars, data is collected for INC: personal income in dollars CRDTLIM: $1 plus the credit limit in dollars available to the individual APR: mean annualized percentage interest rate for borrowing for the individual ADVT: per person advertising expenditure in dollars by manufacturers in the city where the individual lives SEX: gender of the individual; 1 if female, 0 if male A regression analysis was performed with CONS as the dependent variable and CRDTLIM, APR, ADVT, and GENDER as the independent variables. The estimated model was What is the correct interpretation for the estimated coefficient for GENDER? A) Holding the effect of the other independent variables constant, mean personal consumption for females is estimated to be $0.39 higher than males. B) Holding the effect of the other independent variables constant, mean personal consumption for males is estimated to be $0.39 higher than females. C) Holding the effect of the other independent variables constant, mean personal consumption for females is estimated to be 0.39% higher than males. D) Holding the effect of the other independent variables constant, mean personal consumption for males is estimated to be 0.39% higher than females. Answer: A Difficulty: Easy Keywords: dummy variable, slope, interpretation TABLE 14-15 The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), mean teacher salary in thousands of dollars (Salaries), and instructional spending per pupil in thousands of dollars (Spending) of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable, X1 = Salaries and X2 = Spending: 34) Referring to Table 14-15, which of the following is a correct statement? A) The mean percentage of students passing the proficiency test is estimated to go up by 2.79% when mean teacher salary increases by one thousand dollars. B) The mean teacher salary is estimated to go up by 2.79% when mean percentage of students passing the proficiency test increases by 1%. C) The mean percentage of students passing the proficiency test is estimated to go up by 2.79% when mean teacher salary increases by one thousand dollars holding constant the instructional spending per pupil. D) The mean teacher salary is estimated to go up by 2.79% when mean percentage of students passing the proficiency test increases by 1% holding constant the instructional spending per pupil. Answer: C Difficulty: Moderate Keywords: interpretation, slope 35) Referring to Table 14-15, which of the following is a correct statement? A) 18.26% of the total variation in the percentage of students passing the proficiency test can be explained by mean teacher salary and instructional spending per pupil. B) 18.26% of the total variation in the percentage of students passing the proficiency test can be explained by mean teacher salary and instructional spending per pupil after adjusting for the number of predictors and sample size. C) 18.26% of the total variation in the percentage of students passing the proficiency test can be explained by mean teacher salary holding constant the effect of instructional spending per pupil. D) 18.26% of the total variation in the percentage of students passing the proficiency test can be explained by instructional spending per pupil holding constant the effect of mean teacher salary. Answer: A Difficulty: Moderate Keywords: interpretation, coefficient of multiple determination 36) Referring to Table 14-15, which of the following is a correct statement? A) 14.57% of the total variation in the percentage of students passing the proficiency test can be explained by mean teacher salary and instructional spending per pupil. B) 14.57% of the total variation in the percentage of students passing the proficiency test can be explained by mean teacher salary and instructional spending per pupil after adjusting for the number of predictors and sample size. C) 14.57% of the total variation in the percentage of students passing the proficiency test can be explained by mean teacher salary holding constant the effect of instructional spending per pupil. D) 14.57% of the total variation in the percentage of students passing the proficiency test can be explained by instructional spending per pupil holding constant the effect of mean teacher salary. Answer: B Difficulty: Moderate Keywords: interpretation, adjusted r-square 37) Referring to Table 14-15, what is the standard error of estimate? Answer: 5.7351 (%) Difficulty: Easy Keywords: standard error of estimate 38) Referring to Table 14-15, predict the percentage of students passing the proficiency test for a school which has a mean teacher salary of 40,000 dollars, and an instructional spending per pupil of 2,000 dollars. Answer: 39.5127 (%) Difficulty: Easy Keywords: prediction of individual values 39) Referring to Table 14-15, estimate the mean percentage of students passing the proficiency test for all the schools that have a mean teacher salary of 40,000 dollars, and an instructional spending per pupil of 2,000 dollars. Answer: 39.5127 (%) Difficulty: Easy Keywords: estimation of mean values 40) Referring to Table 14-15, which of the following is the correct null hypothesis to test whether instructional spending per pupil has any effect on percentage of students passing the proficiency test, taking into account the effect of mean teacher salary? A) H0 : β0 = 0 B) H0 : β1 = 0 C) H0 : β2 = 0 D) H0 : β3 = 0 Answer: C Difficulty: Easy Keywords: t test on slope, form of hypothesis