QNT 275 Final Exam

  • A Bank with branches in a large metropolitan area is considering opening its offices on Saturday, but it is uncertain whether customers will prefer (1) offering walk-in hours on Saturday or (2) extending branch hours during the week. Listed below are some of the ideas proposed for gathering data. For each, indicate what kind of sampling strategy is involved and what (if any) biases might result.
  • A car manufacturer is concerned that dealers conceal unhappy customers by keeping them out of surveys conducted by the factory. The manufacturer suspects that certain dealers enter incorrect addresses for dissatisfied customers so that they do not receive the satisfaction survey that is mailed by the manufacturer. If a current survey of the 65 customers at a dealership indicates 55% rate its service as exceptionally good, can the manufacturer estimate the proportion of all customers at this dealership who feel that its service is exceptionally good? Can it estimate the proportion at other dealerships?
  • A company buys components from two suppliers. One produces components that are of higher quality than the other. The high-quality supplier, call it Supplier A, has a defect rate of 3%. The low-quality supplier, Supplier B, has a defect rate of 18% but offers lower prices. This company buys in equal volume from both suppliers, with half of the orders going to each supplier.
  • At a large assembly line, the manufacturer reassigns employees to different tasks each month. This keeps the workers from getting bored by endlessly repeating the same task. It also lets them see how the work done in different stages must fit together. It is known that 52% of the employees have less than or equal to two years of experience, 10% have between three and five years of experience, and the rest have more than five years of experience. Assume that teams of three Employees are formed randomly. Dave works at this assembly line.
  • A company tracks the level of sales at retail outlets weekly for 36 weeks. During the first 12 weeks, a fixed level of advertising was used each week to draw in customers. During the second 12 weeks, the level of advertising changed. During the last 12 weeks, a third level of advertising was used. What does the SRM have to say about the average level of sales during these three periods? (Treat sales as Y and advertising as X and think of the data as 36 weeks of information.)
  • Sometimes the volumes of containers are recorded as cubic centimeters, other times as liters. The difference is a factor of 1000. Cubic centimeters are 1000 times the liters. How does this choice affect the estimated value for β1 in a regression that appears in a SRM with the volumes of containers as the response variable y? What about β0 in the SRM?
  • A catalog sales company promises to deliver orders placed on the Internet within three days. Follow-up calls to a few randomly selected customers show that a 95% confidence interval for the proportion of all orders that arrive on time is 90% ± 6%. What does this mean? Are the following conclusions correct?
  • The following item describes a column in a data table. On the basis of the description, assign a one- or two-word name to the variable, indicate its type (categorical, ordinal, or numerical), and describe the cases. If the data are a time series, identify the frequency of the data
  • A contractor built 30 similar homes in a suburban development. The homes have comparable size and amenities, but each has been sold with features that customize the appearance, landscape, and interior. The contractor expects the homes to sell for about $550,000. He expects that one-third of the homes will sell either for less than $475,000 or more than $625,000.
  • Direct mail advertises send solicitations (junk mail) to thousands of potential customers hoping that some will buy the company’s product. The response rate is usually quite low. Suppose a company wants to test the response to a new flyer and sends it to 1,500 randomly selected people. The company gets orders from 115 of the recipients and decides to do a mass mailing list to everyone on its mailing list of over 200,000. Create a 95% confidence interval for the percentage of those people who will order something.
  • The table to the right summarizes results of a survey of the purchasing habits of 1,800 13- to 25-year-olds in a country in 2006, a much sought-after group of customers. Each row of the table indicates the percentage of participants in the survey who say that particular statement.
  • An adjustable rate mortgage allows the rate of interest to fluctuate over the term of the loan, depending on economic conditions. A fixed rate mortgage holds the rate of interest constant. Which sequence of monthly payments has smaller variance, those on an adjustable rate mortgage or those on a fixed rate mortgage?
  • Some electronic devices are better used than new. The failure rate is higher when they are new than when they are six months old. For example, one fourth of the personal music players sold by a particular brand have a flaw. If the player has the flaw, it dies in the first six months. If it does not have this flaw, then only 10% fail in the first six months. Yours dies after you had it for three months. What are the chances that it has this flaw?
  • The Human resources (HR) group gives job applicants at a firm a personality test to assess how well they will fit into the firm and get along with colleagues. Historically, test scores have been normally distributed with mean µ and standard deviation σ = 25. The HR group wants to hire applicants whose true personality rating µ is greater than 172 points. (Test scores are an imperfect measure of true personality.)
  • If the median size used by 450 songs is 3.3 MB, will these all fit on a device that has 2 GB of storage? Can you tell?
  • Count the number of cars that pass by an intersection during consecutive five-minute periods on a highway leading into a city. Would these data allow us to use the law of large numbers eventually to learn P(more than 50 cars in five minutes)?
  • The following item describes a column in a data table. On the basis of the description, assign a one- or two-word name to the variable, indicate its type (categorical, ordinal, or numerical), and describe the cases. If the data are a time series, identify the frequency of the data.
  • Each of the scatterplots below shows a sequence of observations. The x-axis enumerates the sequence. For which cases does the law of large numbers apply to probabilities based on these observations?
  • If the standard deviation of X matches the standard deviation of Y, then what is the relationship between the slope in a least square regression of Y on X and the correlation between x and y?
  • The two pie charts below show the origin of cars bought by customers who traded in models from region A and region B. For example, among those trading in a car produced by a manufacturer in region A, 6% purchased a car made by a manufacturer in region B. What’s the message of these two pie charts?
  • A study revealed surprisingly large differences in rates of lung cancer among smokers of different races. For each group, the study reported a rate among smokers per 100,000. The results are summarized in the table below.
  • The exponentially weighted moving average is a one-sided moving average of the time series. The smoothed value st is an average of yt and prior values. The regular moving average is two sided, averaging values on both sides of yt. A five-term moving average of yt and a seven-term moving average are shown below.
  • In a study how the environment affects spending, researchers varied the presence of music and scents in a shopping mall. Interviews with shoppers who made unplanned purchases revealed the average purchase amounts shown to the right. Each group has 100 Shoppers.
  • Regression models for time series should either use time trends or lags of yt as predictors but never mix the two.
    Is this true or false?
  • An accounting firm is considering offering investment advice in addition to its current focus on tax planning. Its analysis of the costs and benefits of adding this service indicate that it will be profitable if 40% or more of its current customer base use it. The firm plans to survey its customers. Let p denote the proportion of its customers who will use this service if offered, and let p’ denote the proportion who say in a survey that they will use this service. The firm does not want to invest in this expansion unless data show that it will be profitable. Determine whether the following statement is true or false. If the statement is false, explain why it is false.
  • The following item describes a column in a data table. On the basis of the description, assign a one- or two-word name to the variable, indicate its type (categorical, ordinal, or numerical), and describe the cases. If the data are a time series, identify the frequency of the data
  • A business magazine mailed a questionnaire to the human resources directors of the top 200 profitable companies, and received responses from 27% of them. Among those who responded, 40% reported that they did not find that such surveys intruded significantly on their workday.
  • The accompanying histogram shows the distribution of the amount of sales tax in 50 regions.
  • The amount of electricity supplies by a utility to residences in a community during the summer depends on the local weather as well as the habits of the people in the community.
  • If the correlation between X and Y is 0.8 and the slope in the regression of Y on X is 1.4, then which of X or Y has larger variation?
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