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Business and Economic Statistics BAD 2323 Final Exam Part I Multiple Choice 1. A discrete distribution is usually the result of A. a small probability C. a small sample B. a measurement D. a count 2. An event is the collection of one or more A. experiments C. probabilities B. combinations D. outcomes 3. The observation of some activity or the act of taking some measurement is called A. an experiment C. a probability B. an event D. an outcome 4. The mean of a discrete probability is also called the A. expected value C. variance B. standard deviation D. median 5. A listing of all possible outcomes of an experiment and the corresponding probability is called: A. the normal rule C. a probability distribution B. the complementary rule D. a random variable 6. If A and B are mutually exclusive events then P(A or B) equals A. P(A) + P(B) - P(A and B) C. P(A) + P(B) B. P(A) x P(B) D. P(A|B) + P(B|A) 7. If the probability of an event occurring is 0.40, that means A. the event has a 40% chance of not occurring B. the event has a 60% chance of not occurring C. the complement of the event has a 0.40 chance of occurring D. the event has a 30% chance of occurring 8. Which formula represents the probability of the complement of event A? A. 1 + P(A) C. P(A) - 1 B. 1 - P(A) D. P(A) 9. To construct a probability distribution, we need to know A. only the mean C. the size of the sample B. the number of trials and the D. mean and variance are equal probability of success 10. The difference between the binomial and the hypergeometric distribution is A. the trials are not independent for the binomial B. the probability of a success is not the same for all trials in the hypergeometric C. binomial requires a large sample D. the mean and standard deviation are the same for the binomial 11. Which distribution would be most appropriate if one wanted to find the probability of selecting four honest politicians (without replacement) from a sample of 25 politicians? A. Hypergeometric C. discrete B. Binomial D. Poisson 1 Business and Economic Statistics BAD 2323 Final Exam 12. If A and B are independent events, then the probability of A and B equals A. P(A) + P(B) - P(A and B) C. P(A) + P(B) B. P(A) x P(B) D. P(A|B) + P(B|A) 13. Two events occurring at the same time is called A. prior probability C. joint probability B. conditional probability D. subjective probability 14. Which of the following is NOT a requirement for a discrete probability distribution? A. the sum of the probabilities equal to 1.00 B. the outcomes are mutually exclusive C. the trials are independent D. the probability of each outcome is between 0 and 1.00 15. Which of the following is NOT a requirement for the binomial distribution. A. only two outcomes are possible B. the probability of a success changes from one trial to the next C. the sample size must be fixed D. trials must be independent 16. Which of the following statements is true about a poisson distribution? A. the probability of a success is small B. the outcome of one trial affects the outcome of another C. the sample size is large D. the probability changes after each trial E. A & C above 17. The particular result of an experiment is called A. an outcome C. a probability B. combinations D. an experiment 18. Which of the following statements about probability is always correct? A. a probability can range from 0 to 1 B. a probability close to 0 means the event is likely to happen C. a probability close to 1 means the event is NOT likely to happen D. all of the above are correct E. none of the above are correct 19. A probability distribution that can assume only certain values within a range is called: A. a discrete probability distribution B. a continuous probability distribution C. a random variable distribution D. a Poisson probability distribution 20. According to the classical definition of probability A. all events are equally likely B. the probability is based on guesses C. the number of success is divided by the number of successes D. one outcome is exactly three times the next 2 Business and Economic Statistics BAD 2323 Final Exam 21. The normal distribution is A. discrete distribution B. continuous distribution C. asymmetric D. all of the above 22. The correction for continuity is used when A. the distribution is continuous B. the z-scores are less than 0.05 C. the distribution is discrete D. the z-scores are integers 23. A normal distribution is completely described by A. its mean and standard deviation B. its standard deviation C. its mean D. none of the above 24. Any normal distribution can be converted to a standard normal distribution A. A. by finding = B. by determining that is greater than 5 C. by finding D. by calculating the z-value 25. What is the value of the constant e in a Poisson distribution? A. 3.1417 B. 2.678 C. 2.1787 D. 2.71828 26. In a two sample test of means for independent samples, the equal sign always appears in A. The null hypothesis B. The alternative hypothesis C. The upper tail of the test statistic D. None of the above 27. A random sample of 10 observations is selected from the first normal population and 8 from the second normal population. For a one tailed test of hypothesis (.01 significance level) to determine if there is a difference in the population means, degrees of freedom are A. .18 B. 16 C. 17 D. None of the above 28. Which of the following is NOT a requirement for the two sample test of means for independent samples when both samples contain less than 30 observations? A. Equal sample sizes B. Normal population C. Equal population standard deviations D. All of the above are required 29. In a two sample test of means for independent samples, we use the z distribution when A. Both populations are positively skewed B. Population standard deviations are equal C. Both samples are at least 30 D. None of the above 3 Business and Economic Statistics BAD 2323 Final Exam 30. Which of the measures of central tendency is the largest in a positively skewed distribution? A. Mean B. Median C. Mode D. Cannot tell from the information given 31. A discrete variable is A. An example of a qualitative variable B. Can assume only whole numbers C. Can assume only clearly separated values D. Cannot be negative 32. The term ANOVA A. Stands for Another Numerical Observation of the Variance B. Stands for Analysis of Variance C. Has no special meaning D. None of the above 33. The term “Treatment” refers to A. The variation within the cells B. The numerator degrees of freedom C. A source of variation D. None of the above 34. Which level of measurement is required for the mode? A. Nominal B. Ordinal C. Interval D. Ratio 35. In a symmetric distribution A. The mean, median, and mode are all equal B. The median is the largest measure of location C. The mean is the largest measure of location D. The standard deviation is the largest value 36. Which of the following is NOT a characteristic of the F distribution? A. It is positively skewed B. It is based on two sets of degrees of freedom C. It cannot be negative D. It is a discrete distribution 37. The ratio scale of measurement A. Usually involves ranking B. Is usually based on counting C. Has a meaningful zero point D. Cannot assume negative values 38. A disadvantage of the range is A. It does not exist for some sets of data B. It is in different units from the mean C. Only two values are used in its calculation D. All of the above 4 Business and Economic Statistics BAD 2323 Final Exam 39. Which of the following measures of central tendency is affected most by extreme values? A. Mean B. Median C. Mode D. Geometric Mean 40. The standard deviation is A. Based on squared deviations from the mean B. Is in the same units as the mean C. Uses all the observations in its calculation D. All of the above 41. To convert a frequency distribution to a relative frequency distribution A. Multiply the class frequency by 100 B. Divide the lower limit of the first class by the class interval C. Divide the class frequency by the number of observations D. Find the difference between consecutive lower limits 42. The general idea of analysis of variance is to compare estimated variances A. From both between the treatment means and within the treatment means B. Based on several treatments C. From within the treatments D. None of the above 43. The ordinal scale of measurement A. Has a meaningful zero point B. Is based on ranks C. Cannot assume negative values D. All of the above 44. For a 2 goodness-of-fit test A. There is only one degree of freedom B. The rejection region is in the upper right tail C. The scale of measurement is interval D. We must assume a normal population 45. For a 2 goodness-of-fit test A. There is only one degree of freedom B. The rejection region is in the upper right tail C. The scale of measurement is interval D. We must assume a normal population. 46. Which of the following is not a characteristic of the 2 distribution? A. Its shape is based on the sample size. B. It is not negative. C. It is positively skewed. D. It approaches a normal distribution as the degrees of freedom increase. 47. To conduct a nonparametric test the A. Population must follow the normal distribution. B. The standard deviation must be known. C. It is not necessary to make any assumption about the shape of the population. D. The data must be at least interval scale. 5 Business and Economic Statistics BAD 2323 Final Exam 48. In a contingency table A. The number of rows must be the same as the number of columns. B. A variable is classified according to two criteria. C. There must be at least 10 observations in each cell. D. All of the above: 49. In a multiple regression equation there A. Are two or more independent variables. B. Is only one dependent variable. C. Is one intercept value. D. All of the above. 50. A scatter diagram is a chart E. In which the dependent variable is scaled along the vertical axis. A. In which the independent variable is scaled along the horizontal axis. B. That portrays the relationship between two variables. C. All of the above. 51. In correlation analysis A. We consider several independent variables. B. We study the strength of the association between two variables. C. We consider the intercept with the Y-axis. D. None of the above. 52. The sample coefficient of correlation A. Has the same sign as the slope, i.e. b. B. Can range from –1.00 up to 1.00 C. Is also called Pearson's r. D. All of the above. 53. The standard error of the estimate is A. Based on squared deviations from the regression line. B. May assume negative values. C. Is in squared units of the independent variable. D. All of the above. 54. Which of the following is NOT a necessary condition for regression analysis? A. The standard deviation of each of the conditional distributions must be the same. B. The Y values are independent. C. For each X value, there is a group of Y values and these Y values are normally distributed. D. The slope of the regression line is positive (increasing). 55. Which of the following is NOT based on squared deviations from the regression line? A. The coefficient of correlation. B. The coefficient of determination. C. The standard deviation. D. The standard error of estimate. 6 Business and Economic Statistics BAD 2323 Final Exam Part II Problems 1. A retail trade management journal reported that the typical shopper spends an average of 1.80 hours per visit in a shopping mall. A sample of 8 shoppers at the Tupelo Mall revealed the following times. At the 0.01 significance level, can we conclude that shoppers at the Tupelo Mall spend less than a mean of 1.80 hours? 1.4 1.7 1.6 2.1 1.6 1.9 1.7 1.7 a. State the Null and Alternative hypothesis b. State the decision rule c. Compute the value of the test statistic d. Compute the p-value e. What is your decision regarding the null hypothesis? 7 Business and Economic Statistics BAD 2323 Final Exam 2. As part of a safety check, the Mississippi Highway Patrol randomly stopped 65 trucks and checked their tire pressures. The sample mean was 32 pounds per square inch with a sample standard deviation of 2 pounds per square inch. Develop a 98% confidence interval for the population mean. 3. A survey is being conducted on the election of a Student Government President. A pilot survey has determined the variance of the population to be 0.25. If the poll is to have a 98% confidence interval and must be within four percentage points, how many people should be surveyed? 4. Be Fast Oil Changers advertises a mean time of 10 minutes for an oil change with a standard deviation of 3.0 minutes. What percentage of oil changes is completed? Show All work Including graphs. A. Between 10 and 15 minutes B. Less than 12 minutes C. Less than 30 minutes D. Between 12 and 15 minutes E. Twenty percent of their jobs take more than how much time? 8 Business and Economic Statistics BAD 2323 Final Exam 5. According to a recent survey, 70 % of all customers will return to K-Mart. Suppose eight customers are selected at random, what is the probability that : i. A. exactly 5 of the customers will return? ii. all eight will return? iii. At least 7 will return? iv. At least one will return? v. How many customers would be expected to return to Wal-Mart? 6. Is the following sample Positively Skewed? YES NO Explain your answer. 6 12 7 12 8 4 5 9 Business and Economic Statistics BAD 2323 Final Exam Treatment Treatment 1 Treatment 2 3 9 13 10 7 20 9 11 14 15 9 13 14 12 15 10 Anova: Single Factor SUMMARY Groups Count Sum Average Variance Treatment 1 6 58 9.666666667 3.06666667 Treatment 2 4 60 15 11.3333333 Treatment 3 5 63 12.6 8.3 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 70.4 2 35.2 5.11793215 0.024704 3.885294 Within Groups 82.53333 12 6.877777778 Total 152.9333 14 7. Given the above data analysis, List all five steps with appropriate data of the hypothesis test and give your decision. 10 Business and Economic Statistics BAD 2323 Final Exam 8. In the Tupelo, Mississippi TV market there are three commercial television stations, each with its own evening news program from 6:00 until 6:30 P.M. According to a report in this mornings Daily Journal, a random sample of 150 viewers last night revealed 53 watched WTVA (Channel 9), 64 watched WLOV (Channel 13), and 33 watched WCBI (Channel 27). At the .05 significance level, is there a difference in the viewers watching the three channels? Show all five steps. TV Station Frequency WTVA 53 WLOV 64 WCBI 33 9. There are 400 workers employed at Tom’s, Inc. A sample of 30 workers revealed that 18 graduated from Northeast Community College. Construct the 99 percent confidence interval for the proportion of all workers who graduated from Northeast. 10. A recent study of the normal population of American Automobile Dealers Association revealed the mean amount of profit per car sold of a sample of 20 dealers was $290, with a standard deviation of $105. Develop a 95 percent confidence interval for the population mean. 11. 11. A recent study of Northeast students showed that 25% take Spanish, 20% take French, and 10% take both. What percent of students take Spanish or French? 12. The number of claims for missing baggage at the Tupelo airport averages four per Month. What is the probability that in a given month, there will be: a. fewer than 3 claims b. exactly three claims c. three or more claims d. more than three claims 11 Business and Economic Statistics BAD 2323 Final Exam 13. The following data give the daily spending by college students. 271 192 429 205 100 159 321 279 116 363 181 294 279 151 570 90 266 309 240 342 A. How many classes do you recommend? B. What class interval do you recommend? C. What is the lower limit of the first class? D. Organize the data into a Frequency Distribution E. What group or interval has the highest spending habits? 14. The law firm of Yarber and Yarber is located in downtown Doskey Mississippi. There are 10 partners in the firm; 6 live in Booneville and 4 live in Fulton. The managing partner wants to appoint a committee of four partners to look into moving the firm to Tupelo. If the committee is selected at random from the 10 partners, what is the probability that : a. two member live in Booneville and the others live in Fulton? b. at least one member lives in Booneville? 15. Based on a recent survey, 90% of all Wal-Mart customers will use the same store location. If seven customers are selected at random, what is the probability that: a. exactly 4 customers will use the same store? b. less than 2 will use the same store? c. at least one will use the same store? d. How many customers will be expected to use the same store? 12 Business and Economic Statistics BAD 2323 Final Exam 16. A recent article in the Wall Street Journal reported that the 30 year mortgage rate is now less than 6%. A sample of 8 small banks in Mississippi revealed the following 30- year mortgage rates (in percent). 4.8 5.3 6.5 4.8 6.1 5.8 6.2 5.6 At the .01 significance level, can we conclude that the 30-year mortgage rate for small banks is less than 6%? Prove your answer using the five step method and estimate the p-value. 17. The following hypotheses are given: Ho: π = .40 H1: π ≠ .40 A sample of 120 observations revealed that p = .30. At the .05 significance level, can the null hypothesis be rejected? Use the five step method to solve this problem. 18. The null and alternative hypotheses are: Ho: μd ≤ 0 H1: μd > 0 The following sample information shows the number of defective units produced on the day shift and the evening shift for a sample of four days last month. Day 1 2 3 4 Day 10 12 15 16 Evening 8 9 11 16 At the .10 significance level, can we conclude there are more defects produced on the evening shift? Show all five steps. Interpret the results. 19. A sample of 64 observations is selected from a population of men. The sample mean is 2.68 and the sample standard deviation is 0.75. A sample of 49 observations is selected from a population of women. The sample mean is 2.58 and the sample standard deviation is 0.65. Conduct the following test of hypothesis using the .05 significance level. Ho: µ men ≤ µ women H1: µ men > µ women A. Is this a one or two tailed test? B. State the decision rule. C. Compute the value of the test statistic. D. What is your decision regarding the null? 13

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