PAST EXAM 1

SECTION A: ANSWER ALL QUESTIONS.

[20 MARKS]

1. The Graduate Management Admission Test (GMAT) is a standardized test used by schools to determine the aptitude of individuals who are applying for MBA programs. The range of the GMAT score is 200-800. Brian has recently taken the exam and scored 720. This is an example of A) nominal data. B) ordinal data. C) interval data. D) ratio data. 2. A respondent of a survey is asked whether their most recent dining experience was excellent, good, fair, or poor. The person indicates that the experience was "good". This is an example of A) nominal data. B) ordinal data. C) interval data. D) ratio data. 3. The probability that an employee at a company uses illegal drugs is 0.08. The probability that an employee is male is 0.55. Assuming that these events are independent, what is the probability that a randomly chosen employee is a male drug user? A) 0.742 B) 0.145 C) 0.044 D) 0.006 4. If you are interested in comparing variation in sales for small and large stores selling similar goods, which of the following is the most appropriate measure of dispersion? A) the range B) the interquartile range C) the standard deviation D) the coefficient of variation 5. A company has developed a new battery, but the average lifetime is unknown. In order to estimate this average, a sample of 110 batteries is tested and the average lifetime of this sample is found to be 200 hours. The 200 hours is the value of a: A) parameter. B) statistic. C) sampling frame. D) population.

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6. Which of the following statements involve inferential statistics as opposed to descriptive statistics? A) The FAA reported there were 180 near misses among commercial aircraft last year. B) A class of fifty five statistics students earned an average grade of 72.5. C) The city business office reported 50 building permits for new single-family housing units. D) Based on a sample of 450 subscribers, a local satellite TV system estimates that 45 percent of its subscribers watch a premium channel at least once per day. 7. Which of the following statements is incorrect? A) Ordinal data may be described as qualitative. B) Nominal data may be described as quantitative. C) A categorical variable may produce ordinal data. D) A discrete numerical variable may produce ratio scale data. 8. Which of the following is most likely a continuous numerical variable? A) the number of gallons of paint purchased B) the number of reams of paper ordered C) the population of Egypt in 2005 D) the number of miles of interstate highways 9. Which of the following statements involve descriptive statistics as opposed to inferential statistics? A) The Alcohol, Tobacco and Firearms Department reported that Seattle had 1,825 registered gun dealers in 2013. B) Based on a survey of 380 magazine readers, the magazine reports that 30% of its readers prefer double column articles.T C) The FAA samples 425 traffic controllers in order to estimate the percent retiring due to job stress related illness. D) Based on a sample of 350 professional baseball players, a baseball magazine reported that 23% of the parents of all professional baseball players did not play baseball 10. Which of the following is most likely a parameter as opposed to a statistic? A) the average score of the first five students completing an assignment B) the proportion of females registered to vote in a county C) the average height of people randomly selected from a database D) the proportion of trucks stopped yesterday that were cited for bad brakes 11. Tim was planning for a meeting with his boss to discuss a raise in his annual salary. In preparation, he wanted to use the Consumer Price Index to determine the percentage increase in his real (inflation-adjusted) salary over the last three years. Which of the four methods of data collection was involved when he used the Consumer Price Index? A) published sources B) experimentation C) surveying D) observation

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12. When studying the simultaneous responses to two categorical questions, you should set up a A) contingency table. B) frequency distribution table. C) cumulative percentage distribution table. D) histogram. 13. Data on the number of credit hours of 20,000 students at a public university enrolled in a spring semester were collected. Which of the following is the best for presenting the information? A) a pie chart B) a Pareto chart C) a stem-and-leaf display D) a contingency table 14. If two events are collectively exhaustive, what is the probability that one or the other occurs? A) 0 B) 0.50 C) 1.00 D) cannot be determined from the information given 15. If two events are mutually exclusive, what is the probability that both occur at the same time? A) 0 B) 0.50 C) 1.00 D) cannot be determined from the information given 16. The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The probability that neither house sales nor interest rates will increase during the next 6 months is ________. A) 0.11 B) 0.195 C) 0.89 D) 0.90 17. To monitor campus security, the campus police office is taking a survey of the number of students in a parking lot every 30 minutes for a 24-hour period with the goal of determining when patrols of the lot would serve the most students. If X is the number of students in the lot during each period of time, then X is an example of A) a categorical random variable. B) a discrete random variable. C) a continuous random variable. D) a statistic. 3

18. Which measure of central tendency can be used for both numerical and categorical variables? A) arithmetic mean B) median C) mode D) standard deviation 19. The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The probability that both house sales and interest rates will increase during the next 6 months is ________. A) 0.10 B) 0.185 C) 0.705 D) 0.90 20. There are only four 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 four empty rooms be filled with one student per room? A) 330 B) 1,125 C) 7,920 D) 39,916,800

SECTION B: ANSWER ONLY TWO QUESTIONS

[20 MARKS EACH]

Question 1 (a) Why do we have so many different measures of central tendency? Are all really necessary or do they essentially provide the same information? (b) A study of 50 teachers in Kyekyewere showed that 5% of the teachers earn GH¢800.00 per month. State : (i) the variable in the study (ii) the sample size (iii) measurement scale used (c) An investment councilor recently reviewed the account activity of a sample of 10 of his clients and calculated the average number of stock trades per month over the past year for each client. He obtained the following data values: 10.2, 2.5, 11.4, 3.2, 1.1, 3.4, 8.4, 9.7, 11.2, 2.4. Describe the shape of the distribution of the number of trades per month for these 10 clients. 4

Question 2 (a) As a businessperson, in what ways may you find yourself involved with statistics? (b) Consider the problem of a couple planning to have three children, assuming each child born is equally likely to be a boy (B) or a girl (G). (i) List all the possible outcomes in this experiment using a tree diagram. What is the probability of the couple having: (ii) at least two boys (iii) at most one girl (iv) exactly two girls (v) no girl (c) The board of directors of KUKUS Ventures consists of 12 members, 3 of whom are women. A new policy and procedures manual is to be written for the company. A committee of 3 is randomly selected from the board to do the writing. (i) What is the probability that all members of the committee are men? (ii) What is the probability that at least 1 member of the committee is a woman?

Question 3 (a) Why is it necessary for a measure of variation to accompany a measure of central tendency? (b) Out of 6 mathematicians and 8 engineers a committee consisting of 2 mathematicians and 4 engineers is to be formed. In how many ways can this be done if (i) Any mathematician and any engineer can be selected (ii) Two particular mathematicians cannot be on the committee (iii) One particular engineer must be selected. (c) In a contest ,Prince, Mary and James are asked to solve a problem, the respective probabilities that they solve the problem are 0.2, 0.1 and 0.3. Calculate the probability that: (a) they all solve the problem. (b) none of them solves the problem (c) only one of them solves the problem (d) at least one of them solves the problem

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FORMULA SHEET The symbols have their usual meanings. Descriptive Statistics Mean,

Variance

,

Standard Deviation

Coefficient of Variation,

Skewness

Laws of Probability Additive Law: Complement: Independent Events: Conditional Probability:

Counting Principle Combination:

Permutation:

Factorial:

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