statistics-2 by keller.doc

Graphical and Tabular Descriptive Techniques 55 CHAPTER 2GRAPHICAL AND TABULAR DESCRIPTIVE TECHNIQUESSECTIONS 1 MULTIPLE CHOICE QUESTIONSIn the following multiple-choice questions, please circle the correct answer.1.Which of the following statements is false?a. All calculations are permitted on interval datab. All calculations are permitted on nominal datac. The most important aspect of ordinal data is the order of the data valuesd. The only permissible calculations on ordinal data are ones involving a ranking processANSWER:b2.The average number of units earned per semester by college students is suspected to be rising. A researcher at Boston College wishes to estimate the number of units earned by students during the spring semester of 2004 at Boston. To do so, he randomly selects 250 student transcripts and records the number of units each student earned in the spring term of 2004. The variable of interest to the researcher is the a. number of students enrolled at Boston College during the spring term of 2004b. average indebtedness of Boston College students enrolled in the springc. age of Boston College students enrolled in the springd. number of units earned by Boston College students during the spring term of 2004ANSWER:d3.The classification of student major (accounting, economics, management, marketing, other) is an example of a. a categorical random variable.b. a discrete random variablec. a continuous random variabled. a parameter.ANSWER:a4.A study is under way in national forest to determine the adult height of pine trees. Specifically, the study is attempting to determine what factors aid a tree in reaching heights greater than 50 feet tall. It is estimated that the forest contains 32,000 adult pines. The study involves collecting heights from 500 randomly selected adult pine trees and analyzing the results. The variable of interest in the study is the a. age of a pine tree in the national forest.b. height of a pine tree in the national forest.c. number of pine trees in the national forest.d. species of trees in the national forest.ANSWER:b5.The classification of student class designation (freshman, sophomore, junior, senior) is an example of a. a categorical random variable.b. a discrete random variable.c. a continuous random variable.d. a parameter.ANSWER:a6.Most analysts focus on the cost of tuition as the way to measure the cost of a college education. But incidentals, such as textbook costs, are rarely considered. A researcher at Ferris State University wishes to estimate the textbook costs of first-year students at Ferris. To do so, he monitored the textbook cost of 200 first-year students and found that their average textbook cost was $275 per semester. The variable of interest to the researcher is the a. textbook cost of first-year Ferris State University students.b. year in school of Ferris State University students.c. age of Ferris State University students.d. cost of incidental expenses of Ferris State University students.ANSWER:a7.The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a videocassette recorder made by the company over the past 12 months are satisfied with their products. The possible responses to the question “Are you happy, indifferent, or unhappy with the performance per dollar spent on the videocassette recorder?” are values from a a. discrete numerical random variable.b. continuous numerical random variablec. categorical random variable.d. parameter.ANSWER:cTRUE / FALSE QUESTIONS8.There are actually four types of data: nominal, ordinal, interval, and ratio. However, for statistical purposes, there is no difference between interval and ratio data, and the authors of your book combine the two types.ANSWER:T9.Quantitative variables usually represent membership in groups or categories. ANSWER:F 10.Interval data, such as heights, weights, and incomes, are also referred to as quantitative or numerical data. ANSWER:T 11.Nominal data are also called qualitative or categorical data.ANSWER:T 12.ATP singles rankings for tennis players is an example of an interval scale. ANSWER:F13.Interval data may be treated as ordinal or nominal.ANSWER:T 14.Nominal data may be treated as ordinal or intervalANSWER:F15.Professor Hogg graduated from the University of Iowa with a code value = 2 while Professor Maas graduated from Michigan State University with a code value = 1. The scale of measurement likely represented by this information is interval.ANSWER:F16.Ordinal data may be treated as interval but not as nominal.ANSWER:F 17.A variable is some characteristic of a population, while data are the observed values of a variable based on a sample.ANSWER:F18.An automobile insurance agent believes that company “A” is more reliable than company “B”. The scale of measurement that this information represents is the ordinal scale. ANSWER:TSTATISTICAL CONCEPTS & APPLIED QUESTIONS19.The Dean of Students conducted a survey on campus. SAT score in mathematics is an example of a _, or _ variable.ANSWER:quantitative, numerical20.Provide one example for nominal, ordinal, and interval data.ANSWER:Nominal data example: Political party affiliation for voters recorded using the code: 1 = Democrat, 2 = Republican, and 3 = Independent. Ordinal data example: Response to market research survey measured on the Likert scale using the code: 1 = Strongly agree, 2 = Agree, 3 = Neutral, 4 = Disagree, and 5 = Strongly disagree.Interval data example: Temperature in tennis courts during the US Open21.The dean of students conducted a survey on campus. The gender of the student is an example of a _, or _ variable.ANSWER:categorical, qualitative22.For each of the following examples, identify the data type as nominal, ordinal, or interval.a. The letter grades received by students in a computer science classb. The number of students in a statistics coursec. The starting salaries of newly Ph.D. graduates from a statistics programd. The size of fries (small, medium, large) ordered by a sample of Burger King customerse. The college you are enrolled in (Arts and science, Business, Education, etc.) ANSWER:a. Ordinal b. Interval c. Interval d. Ordinal e. Nominal23.The Dean of Students conducted a survey on campus. Class designation (Freshman, Sophomore, Junior, and Senior) is an example of a _, or _ variable.ANSWER:categorical, qualitative24.Most colleges admit students based on their achievements in a number of different areas. The grade obtained in senior level English course (A, B, C, D, or F) is an example of a _, or _ variable.ANSWER:categorical, qualitative25.At the end of an escorted motor coach vacation, the tour operator asks the vacationers to respond to the questions listed below. For each question, determine whether the possible responses are interval, nominal, or ordinal.a. How many escorted vacations have you taken prior to this one?b. Do you feel that the stay in New York was sufficiently long?c. Which of the following features of the hotel in New York did you find most attractive: location, facilities, room size, or price?d. What is the maximum number of hours per day that you would like to spend traveling?e. Would your overall rating of this tour be excellent, good, fair, or poor?ANSWER:a. Intervalb. Nominalc. Nominald. Intervale. Ordinal26.For each of the following, indicate whether the variable of interest would be nominal or interval.a. Whether you are a US citizenb. Your marital statusc. Number of cars in a parking lotd. Amount of time you spend per week on your homework e. Lilys travel time from her dorm to the student union at the university of Iowaf. Heidis favorite brand of tennis balls.ANSWER:a. Nominalb. Nominalc. Intervald. Intervale. Intervalf. Nominal27.In purchasing a used automobile, there are a number of variables to consider. The age of the car is an example of a _, or _ variable.ANSWER:quantitative, numerical28.In purchasing an automobile, there are a number of variables to consider. The body style of the car (sedan, coupe, wagon, etc.) is an example of a _, or _ variable.ANSWER:categorical, qualitative29.Before leaving a particular restaurant, customers are asked to respond to the questions listed below. For each question, determine whether the possible responses are interval, nominal, or ordinal.a. What is the approximate distance of the restaurant from your residence?b. Have you eaten at the restaurant previously?c. On how many occasions have you eaten at the restaurant previously?d. Which of the following attributes of the restaurant do you find most attractive: service, prices, quality of the food, or varied menu?e. Would your overall rating of the restaurant be excellent, good, fair, or poor?ANSWER:a. Intervalb. Nominalc. Intervald. Nominale. OrdinalSECTION 2MULTIPLE CHOICE QUESTIONSIn the following multiple-choice questions, please circle the correct answer.30.The best type of chart for comparing two sets of categorical data is aa. line chartb. pie chartc. histogramd. bar chartANSWER:d31.Which of the following statements about pie charts is false?a. Pie charts are graphical representations of the relative frequency distributionb. Pie charts are usually used to display the relative sizes of categories for interval data. c. Pie charts always have the shape of a circled. Area of each slice of a pie chart is the proportion of the corresponding category of the frequency distribution of a categorical variableANSWER:b32.The two graphical techniques we usually use to present nominal data area. bar chart and histogram b. pie chart and ogivec. bar chart and pie chart d. histogram and ogiveANSWER:c33.Which of the following statements is false?a. A bar chart is similar to a histogramb. A pie chart is a circle subdivided into slices whose areas are proportional to the frequenciesc. Pie charts emphasize the frequency of occurrences of each category in a frequency distributiond. None of the aboveANSWER:c34.Which of the following statements is true?a. Bar charts focus the attention on the frequency of the occurrences of the categoriesb. A bar chart is created by drawing a rectangle representing each categoryc. The height of each rectangle in a bar chart represents the frequency for a particular categoryd. All of the aboveANSWER:dTRUE / FALSE QUESTIONS35.A bar chart is used to represent interval data.ANSWER:F36.One of the advantages of a pie chart is that it clearly shows that the total of all the categories of the pie adds to 100%.ANSWER:T 37.The bar chart is preferred to the pie chart, because the human eye can more accurately judge length comparisons against a fixed scale (as in a bar chart) than angular measures (as in a pie chart).ANSWER:T38.Bar and pie charts are graphical techniques for nominal data. The former focus the attention on the frequency of the occurrences of the categories, and the later emphasize the proportion of occurrences of each category.ANSWER:T 39.Bar and pie charts are two graphical techniques that can be used to represent nominal data.ANSWER:T40.A bar chart is similar to a histogram in the sense that the bases of the rectangles are arbitrary intervals whose centers are the midpoints of the intervals.ANSWER:F41.If we wish to emphasize the relative frequencies for nominal data, we draw a histogram instead of drawing a bar chart.ANSWER:F42.Pie and bar charts are used widely in newspapers, magazines, and business and government reports.ANSWER:T43.The size of each slice in a pie chart is proportional to the percentage corresponding to that category.ANSWER:T44.A category that contains 30% of the observations is represented by a slice of a pie chart that contains 100 degrees.ANSWER:FSTATISTICAL CONCEPTS & APPLIED QUESTIONS45.Identify the type of data for which each of the following graphs is appropriate. a. Pie chartb. Bar chartANSWER:a. Nominal b. Nominal46.Voters participating in a recent election exit poll in Minnesota were asked to state their political party affiliation. Coding the data 1 for Republican, 2 for Democrat, and 3 for Independent, the data collected were as follows: 3, 1, 2,3, 1, 3, 3, 2, 1, 3, 3, 2, 1, 1, 3, 2, 3, 1, 3, 2, 3, 2, 1, 1, and 3. Construct a frequency bar graph.ANSWER:FOR QUESTIONS 47 AND 48, USE THE FOLLOWING NARRATIVE:Narrative: Car DealersCar buyers were asked to indicate the car dealer they believed offered the best overall service. The four choices were Carriage Motors (C), Marco Chrysler (M), Triangle Auto (T), and University Chevrolet (U). The following data were obtained:T C C C U C M T C U U M C M T C M M C MT C C T U M M C C T T U C U T M M C U T47.Car Dealers Narrative Construct a frequency bar chart.ANSWER:48.Car Dealers Narrative Construct a pie chart. Which car dealer offered the best overall service?ANSWER:It seems that Carriage Motors offered the best overall service.49.Given the following five categories and the number of times each occurs, draw a pie chart and a bar chart.Category12345Frequency1530402520ANSWER:FOR QUESTIONS 50 AND 51, USE THE FOLLOWING NARRATIVE:Narrative: Business School GraduatesThe frequency distribution for a sample of 200 business school graduates is shown in the following table.Major of GraduatesNumber of graduatesAccounting58Finance42Management38Marketing52Other10 50.Business School Graduates Narrative Draw a pie chart of the number of graduates.ANSWER:51.Business School Graduates Narrative Draw a frequency bar chart.ANSWER:SECTION 3MULTIPLE CHOICE QUESTIONSIn the following multiple-choice questions, please circle the correct answer.52.The most appropriate type of chart for determining the number of observations at or below a specific value is:a. a histogramb. a pie chartc. a time-series chartd. a cumulative frequency ogiveANSWER:d53.In general, incomes of employees in large firms tend to bea. positively skewedb. negatively skewedc. symmetricd. All of the aboveANSWER:a54.The total area of the bars in a relative frequency histogram:a. depends on the sample sizeb. depends on the number of barsc. depends on the width of each bard. depends on the height of each barANSWER:c55.Which of the following statements is false?a. A frequency distribution counts the number of observations that fall into each of a series on intervals, called classes that cover the complete range of observations.b. The intervals in a frequency distribution may overlap to ensure that each observation is assigned to an intervalc. Although the frequency distribution provides information about how the numbers in the data set are distributed, the information is more easily understood and imparted by drawing a histogramd. The number of class intervals we select in a frequency distribution depends entirely on the number of observations in the data setANSWER:b56.The total area of the five bars in a relative frequency histogram for which the width of each bar is four units is:a. 5b. 4c. 9d. 1ANSWER:b 57.The relative frequency of a class is computed bya. dividing the frequency of the class by the number of classesb. dividing the frequency of the class by the class widthc. dividing the frequency of the class by the total number of observations in the data setd. subtracting the lower limit of the class from the upper limit and multiplying the difference by the number of classesANSWER:c58.A modal class is the class that includes a. the largest number of observationsb. the smallest number of observationsc. the largest observation in the data setd. the smallest observation in the data setANSWER:a59.The sum of the relative frequencies for all classes will always equala. the number of classesb. the class widthc. the total number of observations in the data setd. oneANSWER:d60.When ogives or histograms are constructed, which axis must show the true zero or “origin”?a. The horizontal axis.b. The vertical axis.c. Both the horizontal and vertical axes.d. Neither the horizontal nor the vertical axis.ANSWER:b61.The width of each bar in a histogram corresponds to the a. differences between the lower and upper limits of the class.b. number of observations in each class.c. midpoint of each classd. frequency of observations in each class.ANSWER:a62.The most important and commonly graphical presentation of interval data is aa. bar chartb. histogramc. pie chartd. cumulative frequency distributionANSWER:b 63.According to Sturges rule, the ideal number of class intervals in a frequency distribution of n = 150 data equals abouta. 8b. 15c. 20d. 28ANSWER:a64.According to Sturges rule,