Great Lakes Institute of Management(PGPM 2011-2012) Mid-Term Exam: Time 60 Minutes Statistical Methods for Decision Making Answer as many questions as possible Faculty: P.K. Viswanathan

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Researchers are concerned that the weight of the average American school child is increasing implying, among other things, that children's clothing should be manufactured and marketed in larger sizes. If X is the weight of school children sampled in a nationwide study, then X is an example of A) a categorical random variable. B) a parameter. C) a discrete random variable. D) a continuous random variable. 2) A 99% confidence interval estimate can be interpreted to mean that A) if all possible samples are taken and confidence interval estimates are developed, 99% of them would include the true population mean somewhere within their interval. B) we have 99% confidence that we have selected a sample whose interval does include the population mean. C) Both of the above. D) None of the above. 3) 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 4 methods of data collection was involved when he used the Consumer Price Index? A) Published sources B) Experimentation C) Observation D) Surveying 4) Which of the following is not an element of descriptive statistical problems? A) Identification of patterns in the data. B) The population or sample of interest. C) An inference made about the population based on the sample. D) Tables, graphs, or numerical summary tools. 5) The British Airways Internet site provides a questionnaire instrument that can be answered electronically. Which of the 4 methods of data collection is involved when people complete the questionnaire? A) Observation B) Published sources C) Surveying D) Experimentation 6) The symbol for the power of a statistical test is A) . B) 1 - . 1)

2)

3)

4)

5)

C) .

D) 1 - .

6)

1

7) Suppose a 95% confidence interval for µ has been constructed. If it is decided to take a larger sample and to decrease the confidence level of the interval, then the resulting interval width would __________. (Assume that the sample statistics gathered would not change very much for the new sample.) A) be the same as the current interval width B) be narrower than the current interval width C) be unknown until actual sample sizes and reliability levels were determined D) be larger than the current interval width 8) A Type II error is committed when A) we don't reject a null hypothesis that is true. B) we don't reject a null hypothesis that is false. C) we reject a null hypothesis that is false. D) we reject a null hypothesis that is true. 9) A Type I error is committed when A) we don't reject a null hypothesis that is true. B) we reject a null hypothesis that is true. C) we reject a null hypothesis that is false. D) we don't reject a null hypothesis that is false. 10) Which of the following would be an appropriate null hypothesis? A) The mean of a population is equal to 55. B) The mean of a sample is equal to 55. C) The mean of a population is greater than 55. D) Only A and C are true. 11) The power of a test is measured by its capability of A) not rejecting a null hypothesis that is true. B) rejecting a null hypothesis that is true. C) not rejecting a null hypothesis that is false. D) rejecting a null hypothesis that is false. 12) How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: X = 52, s = 22. Give the null and alternative hypotheses to determine if the number of tissues used during a cold is less than 60.

7)

8)

9)

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11)

12)

A) H0 : X = 52 and H1 : X 52. C) H0 : µ
60 and H1 : µ > 60.

B) H0 : X 60 and H1 : X < 60. D) H0 : µ
60 and H1 : µ < 60.

2

TABLE 2-1 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

13) Referring to Table 2-1, how many total claims are represented in the sample? A) 50 B) 111 C) 250

D) 15

13)

14) 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 A) dot plot. B) pie chart. C) Pareto diagram. D) contingency table. 15) If an economist wishes to determine whether there is evidence that average family income in a community equals $25,000 A) a two-tailed test should be utilized. B) either a one-tailed or two-tailed test could be used with equivalent results. C) a one-tailed test should be utilized. D) None of the above. 16) The width of each bar in a histogram corresponds to the A) differences between the boundaries of the class. B) percentage of observations in each class. C) number of observations in each class. D) midpoint of each class.

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Situation 2-3 Every spring semester, the School of Business coordinates with local business leaders a luncheon 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.

17) Referring to the histogram from Situation 2-3, how many graduating seniors attended the luncheon? A) 152 B) 4 C) 388 D) 275 18) Which of the following statistics is not a measure of central tendency? A) Q3 B) median C) arithmetic mean D) mode 19) Which of the arithmetic mean, median, mode, and geometric mean are resistant measures of central tendency? A) the median and mode only B) the arithmetic mean and mode only C) the mode and geometric mean only D) the arithmetic mean and median only 20) In a right-skewed distribution A) the median equals the arithmetic mean. B) the median is larger than the arithmetic mean. C) the median is less than the arithmetic mean. D) None of the above. 21) Which measure of central tendency can be used for both numerical and categorical variables? A) mode B) median C) arithmetic mean D) geometric mean

17)

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22) In right-skewed distributions, which of the following is the correct statement? A) The arithmetic mean is smaller than the median. B) The mode is larger than the arithmetic mean. C) The distance from Q1 to Q2 is larger than the distance from Q2 to Q3. D) The distance from Q1 to Q2 is smaller than the distance from Q2 to Q3. 23) 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 house sales will increase but interest rates will not during the next 6 months is: A) 0.89 B) 0.51 C) 0.065 D) 0.15 24) 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 events of increase in house sales and no increase in house sales in the next 6 months are A) collectively exhaustive. B) statistically independent. C) mutually exclusive. D) B and C. 25) 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) 0.195 B) 0.89 C) 0.11 D) 0.90 26) The probability that a new advertising campaign will increase sales is assessed as being 0.80. The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.40. Assuming that the two events are independent, the probability that neither the cost is kept within budget nor the campaign will increase sales is: A) 0.32 B) 0.68 C) 0.12 D) 0.88 27) A company has 2 machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces 3 times as many widgets as the older machine does. What is the probability that a randomly chosen widget produced by the company is defective? A) 0.156 B) 0.078 C) 0.310 D) 0.1175

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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: Number of Vehicles Involved 1 2 3 50 100 20 25 175 30 75 275 50

Did alcohol play a role? Yes No Totals

Totals 170 230 400

28) Referring to Table 4-1, what proportion of accidents involved more than one vehicle? A) 275/400 or 68.75% B) 325/400 or 81.25% C) 75/400 or 18.75% D) 50/400 or 12.5% 29) In general, which of the following descriptive summary measures cannot be easily approximated from a box-and-whisker plot? A) the interquartile range B) the variance C) the range D) the median 30) A probability distribution is an equation that A) measures outcomes and assigns values of X to the simple events. B) assigns a value to the variability in the sample space. C) assigns a value to the center of the sample space. D) associates a particular probability of occurrence with each outcome in the sample space. 31) A campus program evenly enrolls undergraduate and graduate students. If a random sample of 4 students is selected from the program to be interviewed about the introduction of a new fast food outlet on the ground floor of the campus building, what is the probability that all 4 students selected are undergraduate students? A) 0.16 B) 1.00 C) 0.0256 D) 0.0625 32) Which of the following about the binomial distribution is not a true statement? A) The probability of success must be constant from trial to trial. B) The random variable of interest is continuous. C) Each outcome may be classified as either "success" or "failure." D) Each outcome is independent of the other. 33) Whenever p = 0.5, the binomial distribution will A) be symmetric only if n is large. C) always be symmetric.

28)

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B) be right-skewed. D) be left-skewed.

33)

34) A professor receives, on average, 24.7 e-mails from students the day before the midterm exam. To compute the probability of receiving at least 10 e-mails on such a day, he will use what type of probability distribution? A) Poisson distribution B) hypergeometric distribution C) binomial distribution D) None of the above.

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35) For some positive value of X, the probability that a standard normal variable is between 0 and +2X is 0.1255. The value of X is: A) 0.99 B) 0.40 C) 0.16 D) 0.32 36) For some positive value of X, the probability that a standard normal variable is between 0 and +1.5X is 0.4332. The value of X is: A) 1.50 B) 0.50 C) 1.00 D) 0.10 37) The local police department must write, on average, 5 tickets a day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 6.5 tickets per day. Interpret the value of the mean. A) The number of tickets that is written most often is 6.5 tickets per day. B) The mean has no interpretation since 0.5 ticket can never be written. C) If we sampled all days, the arithmetic average or expected number of tickets written would be 6.5 tickets per day. D) Half of the days have less than 6.5 tickets written and half of the days have more than 6.5 tickets written. 38) What type of probability distribution will most likely be used to analyze the number of cars with defective radios in the following problem?
From an inventory of 48 new cars being shipped to local dealerships, corporate reports indicate that 12 have defective radios installed. The sales manager of one dealership wants to predict the probability out of the 8 new cars it just received that, when each is tested, no more than 2 of the cars have defective radios. A) hypergeometric distribution B) Poisson distribution C) binomial distribution D) None of the above.

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39) Sampling distributions describe the distribution of A) statistics. C) both parameters and statistics.

B) parameters. D) neither parameters nor statistics.

39)

40) If the expected value of a sample statistic is equal to the parameter it is estimating, then we call that sample statistic A) minimum variance. B) biased. C) unbiased. D) random. 41) For air travelers, one of the biggest complaints is of the waiting time between when the airplane taxis away from the terminal until the flight takes off. This waiting time is known to have a skewed-right distribution with a mean of 10 minutes and a standard deviation of 8 minutes. Suppose 100 flights have been randomly sampled. Describe the sampling distribution of the mean waiting time between when the airplane taxis away from the terminal until the flight takes off for these 100 flights. A) Distribution is skewed-right with mean = 10 minutes and standard error = 0.8 minutes. B) Distribution is approximately normal with mean = 10 minutes and standard error = 8 minutes. C) Distribution is approximately normal with mean = 10 minutes and standard error = 0.8 minutes. D) Distribution is skewed-right with mean = 10 minutes and standard error = 8 minutes.

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42) Sales prices of baseball cards from the 1960s are known to possess a skewed-right distribution with a mean sale price of $5.25 and a standard deviation of $2.80. Suppose a random sample of 100 cards from the 1960s is selected. Describe the sampling distribution for the sample mean sale price of the selected cards. A) normal with a mean of $5.25 and a standard error of $0.28 B) normal with a mean of $5.25 and a standard error of $2.80 C) skewed-right with a mean of $5.25 and a standard error of $2.80 D) skewed-right with a mean of $5.25 and a standard error of $0.28 43) For sample size 16, the sampling distribution of the mean will be approximately normally distributed A) if the sample standard deviation is known. B) if the shape of the population is symmetrical. C) if the sample is normally distributed. D) regardless of the shape of the population. 44) Which of the following statements about the sampling distribution of the sample mean is incorrect? A) The sampling distribution of the sample mean is approximately normal whenever the sample size is sufficiently large (n 30). B) The standard deviation of the sampling distribution of the sample mean is equal to . C) The mean of the sampling distribution of the sample mean is equal to µ. D) The sampling distribution of the sample mean is generated by repeatedly taking samples of size n and computing the sample means. 45) The Central Limit Theorem is important in statistics because A) for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population. B) for a large n, it says the population is approximately normal. C) for any sized sample, it says the sampling distribution of the sample mean is approximately normal. D) for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size. 46) Which of the following is true regarding the sampling distribution of the mean for a large sample size? A) It has the same shape and mean as the population, but has a smaller standard deviation. B) It has a normal distribution with the same mean and standard deviation as the population. C) It has the same shape, mean, and standard deviation as the population. D) It has a normal distribution with the same mean as the population but with a smaller standard deviation. 47) The standard error of the population proportion will become larger A) as the sample size increases. B) as population proportion approaches 0. C) as population proportion approaches 1.00. D) as population proportion approaches 0.50.

42)

43)

44)

45)

46)

47)

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48) The standard error of the mean A) measures the variability of the mean from sample to sample. B) is never larger than the standard deviation of the population. C) decreases as the sample size increases. D) All of the above.
TABLE 2-1

48)

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

49) Referring to Table 2-1, how many drivers are represented in the sample? A) 5 B) 18 C) 50

D) 15

49)

50) If the Type I error ( ) for a given test is to be decreased, then for a fixed sample size n A) the Type II error ( ) will increase. B) a one-tailed test must be utilized. C) the Type II error ( ) will also decrease. D) the power of the test will increase.

50)

9