Sample Midterm I Econ 3790: Business and Economics Statistics Instructor: Yogesh Uppal You are allowed to use a standard size (8.5*11) cheat sheet and a simple calculator. Please write all the answers with a BALL-POINT PEN or an INK PEN. If you have any questions during the exam, please raise your hand. GOOD LUCK!!! I am sure you guys will do great. Multiple Choice Identify the letter of the choice that best completes the statement or answers the question and write it in the space given next to the question number. Each multiple choice question is worth 1 point. 1. In a questionnaire, respondents are asked to mark their gender as male or female. Gender is an example of the a. ordinal scale b. nominal scale c. ratio scale d. interval scale 2. Data obtained from a nominal scale a. must be alphabetic b. can be either numeric or nonnumeric c. must be numeric d. must rank order the data 3. In a post office, the mailboxes are numbered from 1 to 4,500. These numbers represent a. qualitative data b. quantitative data c. either qualitative or quantitative data d. since the numbers are sequential, the data is quantitative 4. A tabular summary of a set of data showing the fraction of the total number of items in several classes is a a. frequency distribution b. relative frequency distribution c. frequency d. cumulative frequency distribution 5. A tabular method that can be used to summarize the data on two variables simultaneously is called a. simultaneous equations b. crosstabulation c. a histogram d. an ogive Exhibit 1-1 A survey of 800 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school. Undergraduate Major Graduate School Business Engineering Others Total Yes 70 84 126 280 No 182 208 130 520 Total 252 292 256 800
6. Refer to Exhibit 1-1. What percentage of the students does not plan to go to graduate school? a. 280 b. 520 c. 65 d. 32 7. Refer to Exhibit 1.1. What percentage of the students' undergraduate major is engineering? a. 292 b. 520 c. 65 d. 36.5 8. Refer to Exhibit 1-1. Of those students who are majoring in business, what percentage plans to go to graduate school? a. 27.78 b. 8.75 c. 70 d. 72.22 9. is an example of a a. population parameter b. sample statistic c. population variance d. mode 10. Which of the following is not a measure of central location? a. mean b. median c. variance d. mode Exhibit 1-2 The weights (in pounds) of a sample of 36 individuals were recorded and the following statistics were calculated. mean = 160 range = 60 mode = 165 variance = 324 median = 170 11. Refer to Exhibit 1-2. The coefficient of variation equals a. 0.1125% b. 11.25% c. 203.12% d. 0.20312% 12. Refer to Exhibit 1-2. The distribution of weights in the above sample is a. positively skewed b. negatively skewed c. symmetric d. None of the above 13. Refer to Exhibit 1-2. The 50th percentile is a. 160 b. 165
c. 170 d. cannot be answered give the amount of information. 14. Refer to Exhibit 1-2. What is the difference between the largest value and the smallest value of the data? a. 160 b. 60 c. 40 d. None of the above 15. Refer to Exhibit 1-2. The standard deviation of the above data is a. 20 b. 18 c. 16 d. 14 16. On a December day, the probability of snow is.30. The probability of a "cold" day is.50. The probability of snow and "cold" weather is.15. Are snow and "cold" weather independent events? a. only if given that it snowed b. no c. yes d. only when they are also mutually exclusive 17. Events A and B are mutually exclusive. Which of the following statements is also true? a. A and B are also independent. b. P(A B) = P(A)P(B) c. P(A B) = P(A) + P(B) d. P(A B) = P(A) + P(B) 18. The sample space refers to a. any particular experimental outcome b. the sample size minus one c. the set of all possible experimental outcomes d. an event 19. Two events are mutually exclusive a. if their intersection is 1 b. if they have no sample points in common c. if their intersection is 0.5 d. None of these alternatives is correct. 20. A method of assigning probabilities based upon judgment is referred to as the a. relative method b. probability method c. classical method d. subjective method 21. The range of probability is a. any value larger than zero b. any value between minus infinity to plus infinity c. zero to one d. any value between -1 to 1 22. The multiplication law is potentially helpful when we are interested in computing the probability of a. mutually exclusive events b. the intersection of two events c. the union of two events d. conditional events 23. If A and B are independent events with P(A) = 0.4 and P(B) = 0.6, then P(A B) =
a. 0.76 b. 1.00 c. 0.24 d. 0.20 24. If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A B) = a. 0.30 b. 0.15 c. 0.00 d. 0.20 25. An experiment consists of four outcomes with P(E 1 ) = 0.2, P(E 2 ) = 0.3, and P(E 3 ) = 0.4. The probability of outcome E 4 is a. 0.500 b. 0.024 c. 0.100 d. 0.900 26. A numerical description of the outcome of an experiment is called a a. descriptive statistic b. probability function c. Variance d. random variable 27. An experiment consists of making 80 telephone calls in order to sell a particular insurance policy. The random variable in this experiment is a a. discrete random variable b. continuous random variable c. complex random variable d. simplex random variable 28. An experiment consists of determining the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is a a. discrete random variable b. continuous random variable c. complex random variable d. simplex random variable 29. Which of the following is not a property of a binomial experiment? a. the experiment consists of a sequence of n identical trials b. each outcome can be referred to as a success or a failure c. the probabilities of the two outcomes can change from one trial to the next d. the trials are independent Exhibit 1.3 The probability that Pete will catch fish when he goes fishing is.8. Pete is going to fish 3 days next week. Define the random variable X to be the number of days Pete catches fish. 30. Refer to Exhibit 1.3. The probability that Pete will catch fish on exactly one day is a..008 b..096 c..104 d..8 31. Refer to Exhibit 1.3. The probability that Pete will catch fish on one day or less is a..008
b..096 c..104 d..8 32. Refer to Exhibit 1.3. The expected number of days Pete will catch fish is a..6 b..8 c. 2.4 d. 3 33. Refer to Exhibit 1.3. The variance of the number of days Pete will catch fish is a..16 b..48 c..8 d. 2.4 Exhibit 1.4 The probability distribution for the number of goals the Lions soccer team makes per game is given below. Number Of Goals Probability 0 0.05 1 0.15 2 0.35 3 0.30 4... 34. Refer to Exhibit 1.4. Fill in the probability of 4 goals per game. a. 0.25 b. 0.35 c. 1.2 d. 0.15 35. Refer to Exhibit 1.4. The standard deviation of number of goals per game is a. 1.06 b. 2.06 c. 3.06
Problem 36. The following data show the yearly salaries of football coaches at some state supported universities. Salary University (in $1,000) A 53 B 44 C 68 D 47 E 62 F 59 G 53 H 94 For the above sample, determine the following measures. a. The mean yearly salary b. The standard deviation c. The mode d. The median e. The 70th percentile. Please interpret your answer. 37. Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A) The probability that you receive an Athletic scholarship is 0.18. The probability of receiving both scholarships is 0.11. The probability of getting Merit scholarship or Athletic scholarship or both is 0.3. a. What is the probability that you will receive a Merit scholarship? b. Are events A and M mutually exclusive? Why or why not? Explain. c. Are the two events A, and M, independent? Explain, using probabilities. 38. A survey of a sample of business students resulted in the following information regarding the genders of the individuals and their selected major. Selected Major Gender Management Marketing Others Total Male 40 10 30 80 Female 30 20 70 120 Total 70 30 100 200 a. What is the probability of selecting an individual who is majoring in Marketing? b. What is the probability of selecting an individual who is majoring in Management, given that the person is female? c. Given that a person is male, what is the probability that he is majoring in Management? d. What is the probability of selecting a male individual?
39. Seventy percent of the students applying to a university are accepted. What is the probability that among the next 10 applicants a. At the most 2 will be accepted? b. Exactly 10 will be accepted? c. Determine the expected number of acceptances d. Compute the standard deviation. 40. A professor at a local university noted that the grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. a. The professor has informed us that 7.93 percent of her students received grades of A. What is the minimum score needed to receive a grade of A? b. Students who made 57.93 or lower on the exam failed the course. What percent of students failed the course? c. If 69.5 percent of the students received grades of C or better, what is the minimum score of those who received C's? Sample Midterm I Answer Section MULTIPLE CHOICE 1. ANS: B 2. ANS: B 3. ANS: A 4. ANS: B 5. ANS: B 6. ANS: C 7. ANS: D 8. ANS: A 9. ANS: A 10. ANS: C 11. ANS: B 12. ANS: B 13. ANS: C 14. ANS: B 15. ANS: B 16. ANS: C 17. ANS: C 18. ANS: C 19. ANS: B 20. ANS: D 21. ANS: C 22. ANS: B 23. ANS: C 24. ANS: C 25. ANS: C 26. ANS: D
PROBLEM 27. ANS: A 28. ANS: B 29. ANS: C 30. ANS: B 31. ANS: C 32. ANS: C 33. ANS: B 34. ANS: D 35. ANS: A 36. ANS: a. 60 b. 15.8 c. 53 d. 56 e. 62. 70% of the universities pay their football coaches yearly salaries less than or equal to $62,000. 37. ANS: a. 0.23 b. No, because P(A M) 0 c. No, because P(A M) P(A) P(B) 38. ANS: a. 0.15 b. 0.25 c. 0.50 d. 0.40 39. ANS: a. 0.0016 (0.0000059049 + 0.000137781 + 0.0014467005) b. 0.028 c. 7 d. 1.45 40. ANS: a. 88.51 b. 8.53% c. 67.39