Sampling and Data: Homework 1.7 2008/03/30 11:45:12 GMT-5 2008/07/03 11:36:41.159 GMT-5 Barbara Illowsky cnx@cnx.org Susan Dean cnx@cnx.org Connexions cnx@cnx.org continuous cumulative data discrete frequency Homework qualitative quantitative random relative sample sampling statistics survey This module presents students with a number of problems related to statistical sampling and data. In particular, students are asked to demonstrate understanding of concepts such as frequency, relative frequency, and cumulative relative frequency, random samples, quantitative vs. qualitative data, continuous vs. discrete data, and other key terms related to sampling and data. Note: This module is currently under revision, and its content is subject to change. This module is being prepared as part of a statistics textbook that will be available for the Fall 2008 semester. For each item below:iIdentify the type of data (quantitative - discrete, quantitative - continuous, or qualitative) that would be used to describe a response. iiGive an example of the data. aNumber of tickets sold to a concert bAmount of body fat cFavorite baseball team dTime in line to buy groceries eNumber of students enrolled at Evergreen Valley College fMost–watched television show gBrand of toothpaste hDistance to the closest movie theatre iAge of executives in Fortune 500 companies jNumber of competing computer spreadsheet software packages Fifty part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below: Part-time Student Course Loads # of Courses Frequency Relative Frequency Cumulative Relative Frequency 1 30 0.6 2 15 3 aFill in the blanks in the table above. bWhat percent of students take exactly two courses? cWhat percent of students take one or two courses? Sixty adults with gum disease were asked the number of times per week they used to floss before their diagnoses. The (incomplete) results are shown below: Flossing Frequency for Adults with Gum Disease # Flossing per Week Frequency Relative Frequency Cumulative Relative Freq. 0 27 0.45 1 18 3 0.93 6 3 0.05 7 1 0.02 aFill in the blanks in the table above. bWhat percent of adults flossed six times per week? cWhat percent flossed at most three times per week? A fitness center is interested in the average amount of time a client exercises in the center each week. Define the following in terms of the study. Give examples where appropriate. aPopulation bSample cParameter dStatistic eVariable fData Ski resorts are interested in the average age that children take their first ski and snowboard lessons. They need this information to optimally plan their ski classes. Define the following in terms of the study. Give examples where appropriate. aPopulation bSample cParameter dStatistic eVariable fData A cardiologist is interested in the average recovery period for her patients who have had heart attacks. Define the following in terms of the study. Give examples where appropriate. aPopulation bSample cParameter dStatistic eVariable fData Insurance companies are interested in the average health costs each year for their clients, so that they can determine the costs of health insurance. Define the following in terms of the study. Give examples where appropriate. aPopulation bSample cParameter dStatistic eVariable fData A politician is interested in the proportion of voters in his district who think he is doing a good job. Define the following in terms of the study. Give examples where appropriate. aPopulation bSample cParameter dStatistic eVariable fData A marriage counselor is interested in the proportion the clients she counsels who stay married. Define the following in terms of the study. Give examples where appropriate. aPopulation bSample cParameter dStatistic eVariable fData Political pollsters may be interested in the proportion of people who will vote for a particular cause. Define the following in terms of the study. Give examples where appropriate. aPopulation bSample cParameter dStatistic eVariable fData A marketing company is interested in the proportion of people who will buy a particular product. Define the following in terms of the study. Give examples where appropriate. aPopulation bSample cParameter dStatistic eVariable fData Airline companies are interested in the consistency of the number of babies on each flight, so that they have adequate safety equipment. Suppose an airline conducts a survey. Over Thanksgiving weekend, it surveys 6 flights from Boston to Salt Lake City to determine the number of babies on the flights. It determines the amount of safety equipment needed by the result of that study. aUsing complete sentences, list three things wrong with the way the survey was conducted. bUsing complete sentences, list three ways that you would improve the survey if it were to be repeated. Suppose you want to determine the average number of students per statistics class in your state. Describe a possible sampling method in 3 – 5 complete sentences. Be detailed. Suppose you want to determine the average number of cans of soda drunk each month by persons in their twenties. Describe a possible sampling method in 3 - 5 complete sentences. Be detailed. 726 distance learning students at Long Beach City College in the 2004-2005 academic year were surveyed and asked the reasons they took a distance learning class. (Source: Amit Schitai, Director of Instructional Technology and Distance Learning, LBCC). The results of this survey are listed in the table below. Reasons for Taking LBCC Distance Learning Courses Convenience 87.6% Unable to come to campus 85.1% Taking on-campus courses in addition to my DL course 71.7% Instructor has a good reputation 69.1% To fulfill requirements for transfer 60.8% To fulfill requirements for Associate Degree 53.6% Thought DE would be more varied and interesting 53.2% I like computer technology 52.1% Had success with previous DL course 52.0% On-campus sections were full 42.1% To fulfill requirements for vocational certification 27.1% Because of disability 20.5% Assume that the survey allowed students to choose from the responses listed in the table above.aWhy can the percents add up to over 100%? bDoes that necessarily imply a mistake in the report? cHow do you think the question was worded to get responses that totaled over 100%? dHow might the question be worded to get responses that totaled 100%? Nineteen immigrants to the U.S were asked how many years, to the nearest year, they have lived in the U.S. The data are as follows: 2 5 7 2 2 10 20 15 0 7 0 20 5 12 15 12 4 5 10 The following table was produced:Frequency of Immigrant Survey Responses Data Frequency Relative Frequency Cumulative Relative Frequency 0 2 2 19 0.1053 2 3 3 19 0.2632 4 1 1 19 0.3158 5 3 3 19 0.1579 7 2 2 19 0.5789 10 2 2 19 0.6842 12 2 2 19 0.7895 15 1 1 19 0.8421 20 1 1 19 1.0000 aFix the errors on the table. Also, explain how someone might have arrived at the incorrect number(s). bExplain what is wrong with this statement: “47 percent of the people surveyed have lived in the U.S. for 5 years.” cFix the statement above to make it correct. dWhat fraction of the people surveyed have lived in the U.S. 5 or 7 years? eWhat fraction of the people surveyed have lived in the U.S. at most 12 years? fWhat fraction of the people surveyed have lived in the U.S. fewer than 12 years? gWhat fraction of the people surveyed have lived in the U.S. from 5 to 20 years, inclusive? A “random survey” was conducted of 3274 people of the “microprocessor generation” (people born since 1971, the year the microprocessor was invented). It was reported that 48% of those individuals surveyed stated that if they had $2000 to spend, they would use it for computer equipment. Also, 66% of those surveyed considered themselves relatively savvy computer users. (Source: San Jose Mercury News) aDo you consider the sample size large enough for a study of this type? Why or why not? bBased on your “gut feeling,” do you believe the percents accurately reflect the U.S. population for those individuals born since 1971? If not, do you think the percents of the population are actually higher or lower than the sample statistics? Why? Additional information: The survey was reported by Intel Corporation of individuals who visited the Los Angeles Convention Center to see the Smithsonian Institure's road show called “America’s Smithsonian.”cWith this additional information, do you feel that all demographic and ethnic groups were equally represented at the event? Why or why not? dWith the additional information, comment on how accurately you think the sample statistics reflect the population parameters. aList some practical difficulties involved in getting accurate results from a telephone survey. bList some practical difficulties involved in getting accurate results from a mailed survey. cWith your classmates, brainstorm some ways to overcome these problems if you needed to conduct a phone or mail survey.

Try these multiple choice questions The next four questions refer to the following: A Lake Tahoe Community College instructor is interested in the average number of days Lake Tahoe Community College math students are absent from class during a quarter. What is the population she is interested in? AAll Lake Tahoe Community College students BAll Lake Tahoe Community College English students CAll Lake Tahoe Community College students in her classes DAll Lake Tahoe Community College math students Consider the following: X = number of days a Lake Tahoe Community College math student is absentIn this case, X is an example of a:AVariable BPopulation CStatistic DData The instructor takes her sample by gathering data on 5 randomly selected students from each Lake Tahoe Community College math class. The type of sampling she used is ACluster sampling BStratified sampling CSimple random sampling DConvenience sampling The instructor’s sample produces an average number of days absent of 3.5 days. This value is an example of a AParameter BData CStatistic DVariable The next two questions refer to the following relative frequency table on hurricanes that have made direct hits on the U.S between 1851 and 2004. Hurricanes are given a strength category rating based on the minimum wind speed generated by the storm. (http://www.nhc.noaa.gov/gifs/table5.gif) Frequency of Hurricane Direct Hits Category Number of Direct Hits Relative Frequency Cumulative Frequency Total = 273 1 109 0.3993 0.3993 2 72 0.2637 0.6630 3 71 0.2601 4 18 0.9890 5 3 0.0110 1.0000 What is the relative frequency of direct hits were category 4 hurricanes? A0.0768 B0.0659 C0.2601 DNot enough information to calculate What is the relative frequency of direct hits were AT MOST a category 3 storm? A0.3480 B0.9231 C0.2601 D0.3370 The next three questions refer to the following: A study was done to determine the age, number of times per week and the duration (amount of time) of resident use of a local park in San Jose. The first house in the neighborhood around the park was selected randomly and then every 8th house in the neighborhood around the park was interviewed. ‘Number of times per week’ is what type of data? Aqualitative Bquantitative - discrete Cquantitative - continuous The sampling method was: Asimple random Bsystematic Cstratified Dcluster ‘Duration (amount of time)’ is what type of data? Aqualitative Bquantitative - discrete Cquantitative - continuous