BANA 2372 - Hollander - Final Exam - Chapters 1-9 - All Practice Questions with Correct Answers. 2022/2023

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BANA 2372 - Hollander - Final Exam - Chapters 1-9 - All Practice Questions with Correct Answers ____ analytics is the set of analytical techniques that yield a course of action. -AnswerPrescriptive ... _____ analytics consists of analytical techniques that use models constructed from past data to predict the future or to assess the impact of one variable on another. -Answerpredictive _____ analytics encompasses the set of analytical techniques that describe what has happened in the past. -Answer- descriptive _____ can be used to determine the percentage of data values that must be within one, two, and three standard deviations of the mean for data having a bell-shaped distribution. -Answer- The empirical rule _____ can be used to make statements about the proportion of data values that must be within a specified number of standard deviations of the mean, regardless of the shape of the distribution. -Answer- Chebyshev's theorem _____ is the process of using procedures from statistics and computer science to extract useful information from extremely large databases. -Answer- data mining A __________ can be used to graphically present quantitative data. -Answer- histogram and a stem-and-leaf display A __________ is a graphical representation in which the sample space is represented by a rectangle and events are represented as circles. -Answer- Venn diagram A (discrete) sample space, denoted S, is a list of all possible outcomes Oi of an experiment. It is denoted as -Answer- S = {??, ??, ... , ??} A board of directors consists of eight men and four women. A four-member search committee is to be chosen at random to recommend a new company president. What is the probability that all four members of the search committee will be women? -Answer- 1/495 or 0.002 A box plot is a graphical representation of data that is based on _____. -Answer- a fivenumber summary A characteristic of interest for the elements is called a(n) _____. -Answer- variable A committee of four is to be selected from a group of 12 people. How many possible committees can be selected? -Answer- 495A common graphical presentation of quantitative data is a _____. -Answer- histogram A company created a side-by-side bar graph to display their projected financing for the next three years. The display is shown below. Which of the following statements is correct? -Answer- The company projects to increase income, while decreasing loans and expenses. A company plans to interview 10 recent graduates for possible employment. The company has three positions open. How many groups of three can the company select? -Answer- 120 A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that 8% of the employees suffered lost-time accidents last year. Management believes that a special safety program will reduce such accidents to 7% during the current year. In addition, it estimates that 15% of employees who had lost-time accidents last year will experience a lost-time accident during the current year. a. What percentage of the employee will experience a lost-time accident in both years? b. What percentage of the employee will experience a lost-time accident over the twoyear period (to 1 decimal)? -Answer- 01.2% Explanation (0.08*0.15) = 0.012 ~ 1.2% 13.8% Explanation 0.08 + 0.07 - 0.012 = 0.138 or 13.8% A conditional probability is computed as -Answer- ? (?|?) =?(? ∩ ?)/?(?) A consulting firm submitted a bid for a large research project. The firm's management initially felt they had a 50-50 chance of getting the project. However, the agency to which the bid was submitted subsequently requested additional information on the bid. Past experience indicates that for 72% of the successful bids and 44% of the unsuccessful bids the agency requested additional information. a. What is the prior probability of the bid being successful (that is, prior to the request for additional information) (to 1 decimal)? b. What is the conditional probability of a request for additional information given that the bid will ultimately be successful (to 2 decimals)? c. Compute the posterior probability that the bid will be successful given a request for additional information (to 2 decimals). -Answer- 0.5 0.72 0.62 A counseling agency has the following data on the gender and marital status of 200 clients: a. If the client was a male, what is the probability that he is single? b. Calculate the probability that a client is female. Calculate the probability that the client is female given that she is married. Are the two events (being a female and being married) dependent or independent? Explain. -Answer- .17 The events are dependent because the calculated probabilities differ.A couple has three children. Assuming each child has an equal chance of being a boy or a girl, what is the probability that they have at least one girl? -Answer- .875 A cumulative relative frequency distribution shows -Answer- the proportion of data items with values less than or equal to the upper limit of each class. A data set has the following five-number summary: {31, 50, 58, 62, and 87}. Which of the following pairs of values in this data set would be considered outliers? -Answer- 31 and 81 A department store has determined in connection with its inventory control that the demand for a certain CD player averages 4 per day. If the store stocks 5 of these items on a particular day, what is the probability that demand will exceed supply? -Answer- .2150 A disadvantage of using an arithmetic mean to summarize a set of data is that __________. -Answer- It can be biased by one or two extremely small or large values A display used to compare the frequency, relative frequency, or percent frequency of two categorical variables is a: -Answer- stacked bar chart. A doctor records a pair of information (temperature when admitted, temperature 24 hours later) for 400 hospital patients selected at random. He finds that the average patients' temperature upon admission is 101 degrees and 99 degrees 24 hours later. The standard deviation is 1.5 degrees for temperatures when admitted and .5 degrees 24 hours later. The correlation between the two temperatures is .8. What is the covariance between the variables? -Answer- .60 A dot plot can be used to display _____. -Answer- the distribution of one quantitative variable A dot plot of the ages of 10 employees of a company is shown below.Ages are rounded to the tens place prior to constructing the graph. What is the shape of the distribution? Explain. -Answer- The distribution of employee ages is skewed to the right because the tail of the distribution extends further toward higher numbers. A frequency distribution is a _____. -Answer- a tabular summary of a set of data showing the number of items in each of several nonoverlapping classes A frequency distribution is a tabular summary of data showing the -Answer- number of items in several classes. A graph with skewness -1.8 would be which of the following? -Answer- highly skewed rightA graphical device for presenting categorical data summaries based on subdivision of a circle into sectors that correspond to the relative frequency for each class is a _____. - Answer- pie chart A graphical device used for enumerating sample points in a multiple-step experiment is a -Answer- None of these alternatives is correct. A graphical device used for enumerating sample points in a multiple-step experiment is a _____. -Answer- tree diagram A graphical display for depicting multiple bar charts on the same display is called a - Answer- side-by-side bar chart. A graphical method of representing the sample points of a multiple-step experiment is a(n) _____. -Answer- tree diagram A graphical method that can be used to show both the rank order and shape of a data set simultaneously is a _____. -Answer- stem-and-leaf display A graphical presentation of a frequency distribution, relative frequency distribution, or percent frequency distribution of quantitative data constructed by placing the class intervals on the horizontal axis and the frequency on the vertical axis is a _____. - Answer- histogram A graphical presentation of the relationship between two quantitative variables is called a: -Answer- scatter diagram. A graphical representation that helps in visualizing a multiple-step experiment is called a -Answer- tree diagram A graphical summary of data that is based on a five-number summary is a _____. - Answer- box plot A group of students had dinner at a local restaurant. The total bill for the dinner was $414.70. Each student paid his/her equal share of the bill, which was $18.85. How many students were at the dinner? -Answer- 22 A histogram displays quantitative data, while a bar graph displays categorical data. - Answer- stem-and-leaf display A histogram is NOT appropriate for displaying which of the following types of information? -Answer- cumulative frequency A histogram is: -Answer- a graphical presentation of a frequency or relative frequency distribution.A joint survey by Parade magazine and Yahoo! found that 59% of American workers say that if they could do it all over again, they would choose a different career (USA Today, September 24, 2012). The survey also found that 33% of American workers say they plan to retire early and 67% say they plan to wait and retire at age 65 or older. Assume that the following joint probability table applies. a. What is the probability a worker would select the same career (to 2 decimals)? b. What is the probability a worker who would select the same career plans to retire early (to 4 decimals)? c. What is the probability a worker who would select a different career plans to retire early (to decimals)? d. What do the conditional probabilities in parts (b) and (c) suggest about the reasons workers say they would select the same career? -Answer- 0.41 0.4878 0.2203 The reasons the worker would select the same career is that there is a greater probability of being able to retire early. A local university administers a comprehensive examination to the recipients of a B.S. degree in Business Administration. A sample of examinations are selected at random and scored. The results are shown below. Grade 93, 65, 80, 97, 85, 87, 97, 60 For the above data, determine a. The mean = b. The median = c. The mode = d. The standard deviation = e. The coefficient of variation = -Answer- 83 86 97 14.01 16.88% A lottery is conducted using three urns. Each urn contains chips numbered from 0 to 9. One chip is selected at random from each urn. The total number of sample points in the sample space is _____. -Answer- 1,000 A magician holds a standard deck of cards and draws one card. The probability of drawing the ace of diamonds is 1/52. What method of assigning probabilities was used? -Answer- Classical method A mean computed in such a way that each data value is given a weight reflecting its importance is referred to as a(n) _____. -Answer- weighted mean A method of assigning probabilities based on historical data is called the -Answerrelative frequency methodA method of assigning probabilities based upon judgment is referred to as the -Answersubjective method A method of assigning probabilities based upon judgment is referred to as the _____. - Answer- None of the answers are correct (below) -relative frequency method -probability method -classical method A method of assigning probabilities which assumes that the experimental outcomes are equally likely is referred to as the -Answer- classical method A national pollster has developed 15 questions designed to rate the performance of the Prime Minister of Canada. The pollster will select 10 of these questions. How many different arrangements are there for the order of the 10 selected questions? -Answer- 10,897,286,400 A numerical measure computed from a sample, such as sample mean, is known as a _____. -Answer- sample statistic A numerical measure of linear association between two variables is the -Answercorrelation coefficient A numerical measure of linear association between two variables is the _____. - Answer- covariance A numerical measure, such as a mean, computed from a population is known as a _____. -Answer- population parameter A numerical value used as a summary measure for a sample, such as sample mean, is known as a -Answer- sample statistic. A perfectly balanced coin is tossed 6 times and tails appears on all six tosses. Then, on the seventh trial -Answer- 1/2 A perfectly balanced coin is tossed 6 times, and tails appears on all six tosses. Then, on the seventh trial -Answer- None of these alternatives is correct. A portion of the population selected to represent the population is called _____. - Answer- a sample A private research organization studying families in various countries reported the following data for the amount of time 4-year-old children spent alone with their fathers each day. Country Time with Dad (minutes) Belgium 30Canada 44 China 54 Finland 50 Germany 36 Nigeria 42 Sweden 46 United States 42 a. The mean = b. The standard deviation = c. The mode = d. The 75th percentile = For the above sample, which is not correct? -Answer- 43 7.56 42 48 The 75th percentile = 49 A probability near one -Answer- indicates an event is almost certain to occur A probability near zero -Answer- indicates an event is quite unlikely to occur A professor rolls a fair, six-sided die. Using the classical method of probability, what is the probability that at least three spots will be showing up on the die? -Answer- 2/3 A recent study found that hamburger fat calories "x" had a positive linear association with the amount of sodium "y" found in that hamburger. This can be interpreted to indicate that -Answer- hamburgers with low amount of fat calories tend to have low amount of sodium. A recent survey finds that 78% of people spend an average of at least 30 minutes per day surfing the internet while they are at work. Let A = Spending an average of at least 30 minutes each day surfing the internet while at work. Which of the following is the complement of A? -Answer- Spending an average of less than 30 minutes per day surfing the internet while at work. A representative of the Environmental Protection Agency wants to select samples from 5 landfills. The Director has 10 landfills from which to collect samples. How many different samples are possible? -Answer- 30,240 A researcher asked 20 people for their zip code. The respondents zip codes are an example of _____. -Answer- categorical data A researcher has collected the following sample data. 5 12 6 8 5 6 7 5 12 4 The 75th percentile is -Answer- 8A researcher has collected the following sample data. 3 5 12 3 2 The mean of the sample is The coefficient of variation is The interquartile range is The range is The standard deviation is The variance is -Answer- 5 81.24% 6 10 4.062 16.5 A researcher has collected the following sample data 5 12 6 8 5 6 7 5 12 4 The 75th percentile is The mean is The median is The mode is -Answer- 8 7 6 5 A researcher has obtained the number of hours worked per week during the summer for a sample of fifteen students. 40 25 35 30 20 40 30 20 40 10 30 20 10 5 20 Using this data set, compute the a. median = b. mean = c. mode = d. 40th percentile = e. range = f. sample variance = g. standard deviation = -Answer- 25 25 20 20 35 128.571 11.339 A researcher is gathering data from four geographical areas designated: South = 1; North = 2; East = 3; West = 4. The designated geographical regions represent _____. - Answer- categorical dataA sample of 9 mothers was taken. The mothers were asked the age of their oldest child. You are given their responses below. 3 12 4 7 14 6 2 9 11 a. Compute the mean = b. Compute the variance = c. Compute the standard deviation = d. Compute the coefficient of variation = e. Determine the 25th percentile = f. Determine the median = g. Determine the 75th percentile = h. Determine the range = -Answer- 7.56 17.78 4.22 55.8 4.0 7.0 11 12 A sample of 15 children gives the name of their favorite restaurants that are as follows: Which of the following is the correct frequency distribution? -Answer- McDonalds 6, Friday's 2, Pizza Hut 2, Mellow Mushroom 2, Luppi's 2, Taco Bell 1 A sample of 50 TV viewers were asked, "Should TV sponsors pull their sponsorship from the programs that draw numerous viewer complaints?" Below are the results of the survey. (Y = Yes; N = No; W = Without Opinion) Which of the following graphical displays is not appropriate to display this data? - Answer- Histogram A sample of 99 distances has a mean of 24 feet and a median of 21.5 feet. Unfortunately, it has just been discovered that an observation that was erroneously recorded as "30" actually had a value of "35." If we make this correction to the data, then -Answer- the median remains the same, but the mean is increased. A sample of charge accounts at a local drug store revealed the following frequency distribution of unpaid balances. Unpaid Balance Frequency 10 - 29 1 30 - 49 6 50 - 69 9 70 - 89 11 90 - 109 13 a. Determine the mean unpaid balance = b. Determine the variance =c. Determine the standard deviation = d. Compute the coefficient of variation = -Answer- 74 533.08 (rounded) 23.09 31.20% A sample of five Fortune 500 companies possessed the following industry codes: banking, banking, finance, retail, and banking. Based on this information, which of the following statements is correct? -Answer- Sixty percent of the sample of five companies are banking industries. A sample of five Fortune 500 companies showed the following revenues ($ millions): 7505.0, 2904.7, 7208.4, 6819.0, and 19500.0. Based on this information, which of the following statements is correct? An estimate of the average revenue for all Fortune 500 companies is -Answer- 8787.42 ($ millions). A sample of single persons receiving Social Security payments revealed these monthly benefits: $826, $699, $1,087, $880, $839, and $965. How many observations are below the median? -Answer- 3 A sample of twelve families was taken. Each family was asked how many times per week they dine in restaurants. Their responses are given below. 2 1 0 2 0 2 1 2 0 2 1 2 Using this data set, compute the a. mode = b. median = c. mean = d. range = e. interquartile range = f. variance = g. standard deviation = h. coefficient of variation = -Answer- 2 1.5 1.25 2 1.5 0.75 0.866 69.28% A sample point refers to a(n) _____. -Answer- individual outcome of an experiment A Scanner Data User Survey of 50 companies found that the average amount spent on scanner data per category of consumer goods was $387,325 (Mercer ManagementConsulting, Inc., April 24, 1997). The $387,325 is an example of _____. -Answer- Both quantitative data and a descriptive statistic are correct. A scatter diagram of the monthly total production costs and the number of units produced at a local company over a period of 10 months is shown below. Comment on any apparent relationship between these two variables. -Answer- There is a positive relationship between the number of units produced and the monthly total production costs. A second useful counting rule enables us to count the -Answer- number of experimental outcomes when n objects are to be selected from a set of N objects. A set of visual displays organizing and presenting information used to monitor the performance of a company or organization in a manner that is easy to read, understand, and interpret is called a _____. -Answer- data dashboard A six-sided die is rolled three times. The probability of observing a 1 three times in a row is _____. -Answer- 1/216 A small town has 5600 residents. The residents in the town were asked whether or not they favored building a new bridge across the river. You are given the following information on the residents' responses, broken down by sex. Men Women In Favor 1400 280 Opposed 840 3080 a. What is the probability that a randomly selected resident is in favor of building the bridge? b. What is the probability that a randomly selected resident is a woman? c. What is the probability that a randomly selected resident is a man and is in favor of building the bridge? -Answer- .30 .60 25 A statistics professor asked students in a class their ages. Based on this information, the professor states that the average age of students in the university is 21 years. This is an example of _____. -Answer- statistical inference A stockbroker placed the following order for a customer: • 50 shares of Kaiser Aluminum at $104 a share • 100 shares of GTE at $25.25 a share • 20 shares of Boston Edison at $9.125 a share What is the weighted arithmetic mean price per share? -Answer- $46.51 A student asked their classmates how tall they are, in which month they were born, and whether they are in a relationship. How many of these variables are quantitative andhow many of these variables are categorical? -Answer- One is quantitative. Two are categorical. A student has selected 8 books that she likes, but she has money only for 3 books. How many possible selections does she have? -Answer- 56 A student has to take seven more courses before she can graduate. If none of the courses are prerequisites to others, how many groups of three courses can she select for the next semester? -Answer- 35 A student made scores of 85, 56, and 91 on her first three statistics tests. What score does she need to make on her next test to have an 80 test average? -Answer- 88 Explanation (85+56+91+x)/(4)=80 = 88 A student was performing an experiment that compared a new high protein food to the old food for pigs. He found the mean weight gain for subjects consuming the new food to be 12.8 pounds with a standard deviation of 3.5 pounds. Later, he realized that the scale was out of calibration by 1.5 pounds (meaning that the scale weighed items 1.5 pounds more). What should be the summary measures, mean and standard deviation, for the subjects consuming the new food? -Answer- The mean should be 11.3 (12.8 minus the overage)and the standard deviation should remain unchanged. A study of 31,000 hospital admissions in New York State found that 4% of the admissions led to treatment-caused injuries. One-seventh of these treatment-caused injuries resulted in death, and one-fourth were caused by negligence. Malpractice claims were filed in one out of 7.5 cases involving negligence, and payments were made in one out of every two claims. a. What is the probability a person admitted to the hospital will suffer a treatmentcaused injury due to negligence (to 2 decimals)? b. What is the probability a person admitted to the hospital will die from a treatment caused injury (to 3 decimals)? c. In the case of a negligent treatment-caused injury, what is the probability a malpractice claim will be paid(to 5 decimals)? -Answer- 0.01 0.006 .00067 A survey item asked students to indicate their class in college: freshman, sophomore, junior, or senior. Which measure(s) of central location would be appropriate for the data generated by that questionnaire item? -Answer- Mode and median A survey of 800 college seniors resulted in the following crosstabulation regarding their undergraduate major and their plan of going to graduate school. According to the crosstabulation above, what percent of college seniors are engineering majors and plan to go to graduate school? -Answer- 10.5%A survey of 800 college seniors resulted in the following crosstabulation regarding their undergraduate major and their plan of going to graduate school. According to the crosstabulation above, what percent of undergraduate majors' plan to go to graduate school? -Answer- 35.0% A survey of 800 college seniors resulted in the following crosstabulation regarding their undergraduate major and their plan of going to graduate school. Compute the row percentages. -Answer- Yes = 35%, No = 65% A survey of 800 college seniors resulted in the following crosstabulation regarding their undergraduate major and their plan of going to graduate school. Of those students who are majoring in Business, what percentage of students plans to go to graduate school? - Answer- 27.78% A survey of a random sample of 100 people was conducted. The participants were asked whether or not they had a dog and whether or not they had allergies. The results are shown below: What percent of the people surveyed have a dog, but do not have allergies? -Answer- 42% A survey of a random sample of 100 people was conducted. The participants were asked whether they had a dog and whether they had allergies. The results are shown below: Compute the row and column totals as well as the row and column percentages. Then determine which of the following statements is correct. -Answer- This crosstabulation shows that those who own a dog are less likely to have allergies than those who do not own a dog. A tabular method that can be used to summarize the data on two variables simultaneously is called _____. -Answer- a crosstabulation A used car salesman has kept records on the customers who visited his showroom. Thirty percent of the people who visited his showroom were female. Furthermore, his records show that 35% of the females who visited his showroom made a purchase , while 20% of the males who visited his showroom made a purchase. Suppose we were told that a customer just made a purchase. What is the probability that the customer was a male? -Answer- 57% P(male | purchase) = P(male and purchase) ÷ P(purchase) = 0.14 / 0.245 = 57% A used car salesman has kept records on the customers who visited his showroom. Thirty percent of the people who visited his showroom were female. Furthermore, his records show that 35% of the females who visited his showroom made a purchase , while 20% of the males who visited his showroom made a purchase. What is the probability that a customer entering his showroom will make a purchase? -Answer- 24.5%A z-score is the number of standard deviations that a value, x, is above or below the mean. Which statement is NOT true -Answer- If the value of x equals the mean, the z score is 1 A(n) _____ is an unusually small or unusually large data value. -Answer- outlier A(n) __________ is a collection of sample points. -Answer- event A(n) __________ is a graph of a cumulative distribution. -Answer- ogive Addition Law -Answer- provides a way to compute the probability that event A or event B or both occur. Used to compute the union of two events. After the data have been arranged from smallest value to largest value, the value in the middle is called the _____. -Answer- median All data collected in a study are referred to as the _____. -Answer- data set All the employees of ABC Company are assigned ID numbers. The ID number consists of the first letter of an employee's last name, followed by four numbers. a.) How many possible different ID numbers are there? b.) How many possible different ID numbers are there for employees whose last name starts with an "A"? -Answer- 260,000 10,000v An element of the sample space is a(n) _____. -Answer- sample point An experiment consists of four outcomes with P(E1) = .2, P(E2) = .3, and P(E3) = .4. The probability of outcome E4 is -Answer- .1 An experiment consists of four outcomes with P(E1) = 0.2, P(E2) = 0.3, and P(E3) = 0.4. The probability of outcome E4 is -Answer- 0.100 An experiment consists of rolling two fair six-sided dice and finding the sum of the spots. How many outcomes are in the sample space? What is the probability of rolling a sum of 12? -Answer- 1/36 An experiment consists of selecting a student body president and vice president. All undergraduate students (freshmen through seniors) are eligible for these offices. How many sample points (possible outcomes as to the classifications) exist? -Answer- 16 An experiment consists of selecting a student body president, vice president, and a treasurer. All undergraduate students, freshmen through seniors, are eligible for the offices. How many sample points (possible outcomes as to the classifications) exist? - Answer- 64An experiment consists of three steps. There are four possible results on the first step, three possible results on the second step, and two possible results on the third step. The total number of experimental outcomes is _____. -Answer- 24 An experiment consists of tossing four coins successively. The number of sample points in this experiment is _____. -Answer- 16 An important measure of location for categorical data is the _____. -Answer- mode An important numerical measure related to the shape of a distribution is the _____. - Answer- skewness An overnight express company must include five new cities on its routes. How many different routes possible, assuming that it does not matter in which order the cities are included in the routing? -Answer- 120 Any process that generates well-defined outcomes is _____. -Answer- an experiment Arithmetic operations are inappropriate for _____. -Answer- categorical data Assume a student received the following grades for the semester: History, B; Statistics, A; Spanish, C; and English, C. History and English are 5 credit-hour courses, Statistics a 4 credit-hour course, and Spanish is a 3 credit-hour course. If 4 grade points are assigned for an A, 3 for a B, and 2 for a C, what is the weighted mean grade for the semester? -Answer- 2.76 Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = 0.25 and P(B) = 0.75 If an amount is zero, enter "O". a. What is P(A ∩ B)? b. What is P(A│B)? c. A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive, they must be independent. Is this statement accurate? d. What general conclusion would you make about mutually exclusive and independent events given the results of this problem? -Answer- 0 0 No Mutually exclusive events are dependent Assume you have applied for two jobs A and B. Getting an offer for job A has no influence on whether or not you receive an offer for job B and vice versa. The probability that you get an offer for job A is .51. The probability of being offered job B is .33. What is the approximate probability that you do not get either job? -Answer- .328 P(Ac).P(Bc) = (0.49)(0.67) = .328Assume your favorite football team has 3 games left to finish the season. The outcome of each game can be win, lose, or tie. How many possible outcomes exist? -Answer- 27 Assume your favorite football team has two games left to finish the season. The outcome of each game can be win, lose, or tie. The number of possible outcomes is _____. -Answer- 9 Assuming that each of the 52 cards in an ordinary deck has a probability of 1/52 of being drawn, what is the probability of drawing a black ace? -Answer- 2/52 Assuming the distribution is normally distributed with mean of 40 and standard deviation of 4, calculate the X values whose z-scores are -1 and -1.5 respectively. -Answer- 36 and 34 Assuming the distribution is normally distributed with mean of 66 and standard deviation of 2, calculate the z-score for X = 68 and X = 69, respectively. -Answer- 1 and 1.5 Basic Requirements for Assigning Probabilities -Answer- The probability assigned to each experimental outcome must be between 0 and 1, inclusively Bayes' Theorem -Answer- provides the means for revising the prior probabilities. Bayes' theorem is applicable when the events for which -Answer- we want to compute posterior probabilities are mutually exclusive and their union is the entire sample space. Bayes' theorem is used to compute -Answer- posterior probabilities of an event and its complement. Bayes' Theorem often we begin probability analysis with initial or -Answer- prior probabilities Bayes' Theorem Tabular Approach Column 1 Tabular Approach Column 2 Tabular Approach Column 3 -Answer- The mutually exclusive events for which posterior probabilities are desired. The prior probabilities for the events. The conditional probabilities of the new information given each event Before drawing any conclusions about the relationship between two variables shown in a crosstabulation, you should _____. -Answer- investigate whether any hidden variables could affect the conclusions Below you are given the ages of a sample of 10 college students who are enrolled in statistics 20 18 20 22 18 20 22 17 19 24a. Compute the mean = b. Compute the variance = c. Compute the standard deviation = d. Compute the coefficient of variation = e. Determine the 25th percentile = f. Determine the median = g. Determine the 75th percentile = h. Determine the range = -Answer- 20 4.667 2.16 10.8% 18 20 22 7 Categorical data _____. -Answer- may be either numeric or nonnumeric Categorical data can be graphically represented by using a(n) _____. -Answer- bar chart Categorical data use either the ______ or ______ scale of measurement. -Answernominal; ordinal Chebyshev's theorem requires that z be _____. -Answer- greater than 1 Classical Approach Example: #2 Texas Lottery Pick 3: You can choose 3 numbers. If your numbers are drawn, you win! Probabilities depend on whether you restrict yourself to -Answer- 3 different numbers or allow duplicates. Classical Method -Answer- Assigning probabilities based on the assumption of equally likely outcomes. Classical method Example: Rolling a Die, If an experiment has n possible outcomes, the classical method will assign a probability of 1/n to each outcome. Sample Space: S = {1, 2, 3, 4, 5, 6} Probabilities: -Answer- Each sample point has a 1/6 chance of occurring College students were surveyed to determine how much they planned to spend in various categories during the upcoming academic year. One category is the amount spent on school supplies. The graphs below show the amount of money spent on school supplies by women and men. Approximately what percent of women spend more than $105 on school supplies? -Answer- 5% Compute the weighted mean for the following data.xi Weight (wi ) 9 10 8 12 5 4 3 5 2 3 -Answer- 6.676 Compute the weighted mean for the following data. xi Weight (wi ) 19 12 17 30 14 28 13 10 18 10 -Answer- 16 Consider a sample with the following data values. 462 490 350 294 574 Compute the Z scores for the above five observations. Mean = 434 Standard Deviation = 112 X Z-Score -Answer- X Z-Score 462 0.25 490 0.5 350 0.75 294 1.25 574 1.25 Consider the data in the following frequency distribution. Assume the data represen t a population. Class Frequency 2 - 6 2 7 - 11 3 12 - 16 4 17 - 21 1 For the above data, which is correct? The mean = The variance = The standard deviation = -Answer- 11 21 4.58Consider the experiment of flipping a coin four times. How many outcomes are in the sample space? If needed, create a tree diagram to help answer the question. -Answer- 16 Consider these parallel boxplots of gasoline mileage for three makes of cars. Which of the following are true statements? I. All three have the same range. II. All three have the same interquartile range. III. The difference in the medians between the first and third distributions is equal to the interquartile range of the second distribution. -Answer- I and III Continuous random variable -Answer- may assume any numerical value in an interval or collection of intervals Counting Rule for Combinations -Answer- Number of Combinations of N objects taken n at a time Counting Rule for Combinations equation -Answer- N!/n!(N-n)! Counting Rule for Permutations -Answer- A third useful counting rule enables us to count the number of experimental outcomes when n objects are to be selected from a set of N objects, where the order of selection is important. Counting Rule for Permutations equation -Answer- N!/(N-n) Data collected at the same, or approximately the same, point in time are _____ data - Answer- cross-sectional Data collected over several time periods are _____ data. -Answer- time series Data on U.S. work-related fatalities by cause follow (The World Almanac, 2012). Cause of Fatality Number of Fatalities Transportation incidents 1795 Assaults and violent acts 837 Contact with objects and equipment 741 Falls 645 Exposure to harmful substances or environments 404 Fires and explosions 113 Assume that a fatality will be randomly chosen from this population. Round your answers to four decimal places. a. What is the probability the fatality resulted from a fall? b. What is the probability the fatality resulted from a transportation incident? c. What cause of fatality is least likely to occur? d. What is the probability the fatality resulted from this cause? -Answer- .1422.3958 Fires and Explosions .0249 Data that provide labels or names for groupings of like items are known as _____. - Answer- categorical data Discrete random variable -Answer- may assume either a finite number of values or an infinite sequence of values Discrete uniform probability distribution -Answer- is the simplest example of a discrete probability distribution given by a formula f(x) = 1/n Discrete uniform probability distribution n = -Answer- the number of values the random variable may assume The values of the random variable are equally likely. Do you think global warming will have an impact on you during your lifetime? A CBS News/New York Times poll of 1000 adults in the United States asked this question (CBS News website, December, 2014). Consider the responses by age groups shown below. Age Response 18-29 30+ Yes 134 293 No 131 432 Unsure 2 8 a. What is the probability that a respondent 18-29 years of age thinks that global warming will not pose a serious threat during his/her lifetime (to 4 decimals)? b. What is the probability that a respondent 30+ years of age thinks that global warming will not pose a serious threat during his/her lifetime (to 4 decimals)? c. For a randomly selected respondent, what is the probability that a respondent answers yes (to 3 decimals)? d. Based on the survey results, does there appear to be a difference between ages 18- 29 and 30+ regarding concern over global warming? -Answer- .4906 .5894 .427 There is a 9.88% difference between the two. Dr. Kurt Thearling, a leading practitioner in the field, defines data mining as "the _____ extraction of _____ information from databases." -Answer- automated, predictive During a cold winter, the temperature stayed below zero for 10 days (ranging from -20 to -5). The variance of the temperatures of the 10 day period _____. -Answer- must be at least zeroDuring the first three semesters of studies, 88% of the UC COBA students take ACCT1, 75% take bothACCT1 and STAT1, and 91% take at least one of the two courses. What is the probability that a randomly selected UC COBA student takes STAT1 during his/her first three semesters? -Answer- 0.78 During the first two years of studies, 82% of the UT COBI students take BUAD 2040, 66% take BUAD2060, and 88% take at least one of the two courses. What is the probability that a randomly selected UT COBI student takes both these courses during his/her first two years of studies? -Answer- 0.60 Each customer entering a department store will either buy or not buy some merchandise. An experiment consists of following 4 customers and determining whether or not they purchase any merchandise. How many sample points exist in the above experiment? (Note that each customer is either a purchaser or non-purchaser.) - Answer- 16 Each customer entering a department store will either buy or not buy some merchandise. An experiment consists of following three customers and determining whether or not they purchase any merchandise. The number of sample points in this experiment is _____. -Answer- 8 Each individual outcome of an experiment is called -Answer- sample point Events A and B are mutually exclusive if their joint probability is -Answer- zero Events A and B are mutually exclusive with P(A) = .3 and P(B) = .2. The probability of the complement of event B equals _____. -Answer- None of the answers are correct (below), 0, .06, .70 Events A and B are mutually exclusive with P(A) = 0.3 and P(B) = 0.2. Then, P(Bc) = - Answer- 0.8 Events A and B are mutually exclusive. Which of the following statements is also true? - Answer- P(A ∪ B) = P(A) + P(B) Events that have no sample points in common are -Answer- mutually exclusive events Excel's _____ function can be used to compute the data value occurring most frequently. -Answer- MODE.SNGL Excel's _____ function can be used to compute the mean. -Answer- AVERAGE Excel's _____ function can be used to compute the middle value of an ordered data set. -Answer- MEDIANExcel's _____ function can be used to compute the population standard deviation. - Answer- STDEV.P Excel's _____ function can be used to compute the population variance. -AnswerVAR.P Excel's _____ function can be used to compute the sample correlation coefficient. - Answer- CORREL Excel's _____ function can be used to compute the sample covariance. -AnswerCOVARIANCE.S Excel's _____ function can be used to compute the sample standard deviation. - Answer- STDEV.S Excel's _____ function can be used to compute the sample variance. -Answer- VAR.S Excel's __________ can be used to construct a crosstabulation. -Answer- PivotTable report Excel's __________ can be used to construct a frequency distribution for categorical data. -Answer- COUNTIF function Excel's Chart Tools can be used to construct a _____. bar chart pie chart histogram All of these can be constructed using Excel's Chart Tools. -Answer- All of these can be constructed using Excel's Chart Tools. Excel's Chart Tools does NOT have a chart type for constructing a _____. -Answerstem-and-leaf display Expected value, or mean, of a random variable is a measure of its -Answer- central location. Facts and figures collected, analyzed, and summarized for presentation and interpretation are called _____. -Answer- data Fifteen percent of the students in a School of Business Administration are majoring in Economics, 20% in Finance, 35% in Management, and 30% in Accounting. The graphical device(s) that can be used to present these data is(are) _____. -Answer- both a bar chart and a pie chartFifty voters registered as democrats were asked, "Do you think the current frontrunner should receive the nomination for president from the Democratic Party?" Their responses are displayed in the bar graph below. Based upon the bar graph we can observe that -Answer- 48% of the democratic voters polled do not believe that the current frontrunner should receive the nomination for president from the Democratic Party. Flight time from Cincinnati to Atlanta is an example of a _____ variable and _____ measurement. -Answer- continuous; ratio For a data set with an odd number of observations that have been sorted from smallest to largest values, where is the median located? -Answer- (n+1)/2 For a data set, half of the observations are always greater than the ____. -AnswerMedian For any data set, which measures of central location have only one value? -AnswerMean and median For ease of data entry into a university database, 1 denot [Show More]

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