A test for AIDS is 99% successful, i.e. if you are HIV+, it will be detected in 99% of all tests, and if you are not, it will again be right 99% of the time. Assume that about 1% of the population are HIV+. You take part in a random testing procedure, which gives a positive result. What is the probability that you are HIV+? What implications does your result have for AIDS testing?
> Lottery tickets are sold in different outlets: supermarkets, smaller shops and outdoor kiosks. Sales were sampled from several of each of these, with the following results: Does the evidence indicate a significant difference in sales? Use the 5% signif
> An example in Chapter 5 compared R&D expenditure in Britain and Germany. The sample data were: Is there evidence, at the 5% significance level, of difference in the variances of R&D expenditure between the two countries? What are the implicatio
> Given the following data on two sample variances, test whether there is any significant difference. Use the 1% significance level. si = 55 s3 = 48 ni 25 n2 30
> A roadside survey of the roadworthiness of vehicles obtained the following results: Is there any association between the type of vehicle and the likelihood of it being unfit for the road? Roadworthy Not roadworthy Private cars 114 30 Company cars 8
> What is the power of the test carried out in Problem 5.3? Data from Problem 5.3: A coin which is either fair or has two heads is to be tossed twice. You decide on the following decision rule: if two heads occur you will conclude it is a two-headed coin
> Using the data from Problem 1.14: Data from Problem 1.14: The table below shows the different categories of investment in the United Kingdom over a series of years: Use appropriate graphical techniques to analyse the properties of any one of the inve
> Testing the null hypothesis that μ= 10 against m > 10, a researcher obtains a sample mean of 12 with standard deviation 6 from a sample of 30 observations. Calculate the z score and the associated Prob-value for this test.
> Computer diskettes (the precursor to USB drives) which do not meet the quality required for high density diskettes are sold as low-density diskettes (storing less data) for 80 pence each. High-density diskettes are sold for £1.20 each. A firm samples 30
> In comparing two medical treatments for a disease, the null hypothesis is that the two treatments are equally effective. Why does making a Type I error not matter? What significance level for the test should be set as a result?
> a. A consumer organisation is testing two different brands of battery. A sample of 15 of brand A shows an average useful life of 410 hours with a standard deviation of 20 hours. For brand B, a sample of 20 gave an average useful life of 391 hours with st
> Two samples are drawn. The first has a mean of 150, variance 50 and sample size 12. The second has mean 130, variance 30 and sample size 15. Test the hypothesis that they are drawn from populations with the same mean.
> A photo processing company sets a quality standard of no more than 10 complaints per week on average. A random sample of 8 weeks showed an average of 13.6 complaints, with standard deviation 5.3. Is the firm achieving its quality objective?
> Consider the investor in the text, seeking out companies with weekly turnover of at least £5000. He or she applies a one-tail hypothesis test to each firm, using the 5% significance level. State whether each of the following statements is true or false (
> a. A random sample of 20 observations yielded a mean of 40 and standard deviation 10. Test the hypothesis that μ= 45 against the alternative that it is not. Use the 5% significance level. b. What assumption are you implicitly making in carrying out this
> A transport company wants to compare the fuel efficiencies of the two types of lorry it operates. It obtains data from samples of the two types of lorry, with the following results: Test the hypothesis that there is no difference in fuel efficiency, us
> Given the following data from two independent samples: test the hypothesis of no difference between the population means against the alternative that the mean of population 1 is greater than the mean of population 2. X1 = 115 X2 = 105 S1 = 21 S2 =
> Using the data from Problem 1.13: Data from Problem 1.13: The following data show car registrations in the United Kingdom for 1987–2010: a. Calculate the average rate of growth of the series. b. Calculate the standard deviation arou
> Test the hypothesis that 10% of your class or lecture group are left-handed.
> Test H0: π = 0.5 against H0: π ≠ 0.5 using p = 0.45 from a sample of size n = 35.
> From experience it is known that a certain brand of tyre lasts, on average, 15 000 miles with standard deviation 1250. A new compound is tried and a sample of 120 tyres yields an average life of 15 150 miles, with the same standard deviation. Are the new
> Given the following sample data: test the null hypothesis that the true mean is equal to 12, against a two-sided alternative hypothesis. Draw the distribution of x under the null hypothesis and indicate the rejection regions for this test. X = 15 s
> Given the sample data p = 0.4, n = 50, calculate the 99% confidence interval estimate of the true proportion.
> a. A random sample of 100 record shops found that the average weekly sale of a particular CD was 260 copies, with standard deviation of 96. Find the 95% confidence interval to estimate the true average sale for all shops. b. To compile the CD chart it is
> Given the sample data calculate the 99% confidence interval estimate of the true mean. If the sample size were 20, how would the method of calculation and width of the interval be altered? X = 40 s = 10 n = 36
> Following the previous question, prove that the most precise unbiased estimate is obtained by setting w1 = w2 = 1 2 . (Hint: Minimise V (w1x1 + w2x2) with respect to w1 after substituting w2 = 1 - w1. You will need a knowledge of calculus to solve this.
> A random sample of two observations, x1 and x2, is drawn from a population. Prove that w1x1 + w2x2 gives an unbiased estimate of the population mean as long as w1 + w2 = 1. (Hint: Prove that E (w1x1 + w2x2) = m.)
> Explain why an unbiased estimator is not always to be preferred to a biased one.
> The table below shows the different categories of investment in the United Kingdom over a series of years: Use appropriate graphical techniques to analyse the properties of any one of the investment series. Comment upon the results. (Although this seem
> Explain the difference between an estimate and an estimator. Is it true that a good estimator always leads to a good estimate?
> The heights of 10 men and 15 women were recorded, with the following results: Estimate the true difference between men’s and women’s heights. Use the 95% confidence level. Mean Variance Men 173.5 80 Women 162 65
> Two samples were drawn, each from a Normally distributed population, with the following results: Estimate the difference between the population means, using the 95% confidence level. X1 = 45 X2 = 52 S1 = 8 %3D ni = 12 $2 = 5 n2 = 18
> A sample of 12 families in a town reveals an average income of £25 000 with standard deviation £6000. Why might you be hesitant about constructing a 95% confidence interval for the average income in the town?
> A sample of 16 observations from a Normally distributed population yields a sample mean of 30 with standard deviation 5. Find the 95% confidence interval estimate of the population mean.
> Sixty-seven percent out of 150 pupils from school A passed an exam; 62% of 120 pupils at school B passed. Estimate the 99% confidence interval for the true difference between the proportions passing the exam.
> Given the sample data estimate the true difference between the means with 95% confidence. X1 = 25 X2 = 22 S2 = 18 = 100 %3D S1 = 12 ni = 80 n2
> A political opinion poll questions 1000 people. Some 464 declare they will vote Conservative. Find the 95% confidence interval estimate for the Conservative share of the vote.
> Six dice are rolled and the number of sixes is noted. Calculate the probabilities of 0, 1, . . ., 6 sixes and graph the probability distribution.
> Sketch the probability distribution for the number of accidents on the same stretch of road in one year. How and why does this differ from your previous answer?
> The following data show car registrations in the United Kingdom for 1987–2010: a. Draw a time-series graph of car registrations. Comment upon the main features of the series. (It looks daunting, but it will take you less than 10 minut
> This problem demonstrates the Central Limit Theorem at work. In your spreadsheet, use the = RAND ( ) function to generate a random sample of 25 observations (I suggest entering this function in cells A4:A28, for example). Copy these cells across 100 colu
> A coin is tossed 10 times. Write down the distribution of the number of heads, (a) exactly, using the Binomial distribution, (b) approximately, using the Normal distribution. (c) Find the probability of four or more heads, using both methods. How accurat
> If x ∼ N (10, 9), find (a). Pr (x > 12) (b). Pr (x < 7) (c). Pr (8 < x < 15) (d). Pr (x = 10)
> A multiple choice test involves 20 questions, with four choices for each answer. a. If you guessed the answers to all questions at random, what mark out of 20 would you expect to get? b. If you know the correct answer to eight of the questions, what is y
> Criticise the following statistical reasoning. The average price of a dwelling is £54 150. The average mortgage advance is £32 760. So, purchasers have to find £21 390, that is, about 40% of the purchase price. On any basis, that is an enormous outlay wh
> Demonstrate, using Σ notation, that V(kx) = k2V(x).
> Demonstrate, using Σ notation, that E (x + k) = E(x) + k.
> A four-engine plane can fly as long as at least two of its engines work. A two-engine plane flies as long as at least one engine works. The probability of an individual engine failure is 1 in 1000. a. Would you feel safer in a four- or two-engine plane,
> A firm employing 100 workers has an average absenteeism rate of 4%. On a given day, what is the probability of (a). no workers, (b). one worker, (c). more than six workers being absent?
> The UK record for the number of children born to a mother is 39, 32 of them girls. Assuming the probability of a girl in a single birth is 0.5 and that this probability is independent of previous births: (a) Find the probability of 32 girls in 39 births
> A coin is either fair or has two heads. You initially assign probabilities of 0.5 to each possibility. The coin is then tossed twice, with two heads appearing. Use Bayes’ theorem to work out the posterior probabilities of each possible outcome.
> The average income of a country is known to be £10 000 with standard deviation £2500. A sample of 40 individuals is taken and their average income calculated. (a) What is the probability distribution of this sample mean? (b) What is the probability of th
> The French national lottery works as follows. Six numbers from the range 0 to 49 are chosen at random. If you have correctly guessed all six, you win the first prize. What are your chances of winning if you are allowed to choose only six numbers? A singl
> IQ (the intelligence quotient) is Normally distributed with mean 100 and standard deviation 16. (a) What proportion of the population has an IQ above 120? (b) What proportion of the population has an IQ between 90 and 110? (c) In the past, about 10% of t
> Manchester United beat Liverpool 4–2 at soccer, but you do not know the order in which the goals were scored. Draw a tree diagram to display all the possibilities and use it to find (a) the probability that the goals were scored in the order L, MU, MU, M
> Find the values of z which cut off (a) the top 10% (b) the bottom 15% (c) the middle 50% of the standard Normal distribution.
> Which of the following events are independent? a. Two flips of a fair coin. b. Two flips of a biased coin. c. Rainfall on two successive days. d. Rainfall on St. Swithin’s Day and rain one month later.
> On a test taken by 100 students, the average mark is 65, with variance 144. Student A scores 83; student B scores 47. a. Calculate the z scores for these two students. b. What is the maximum number of students with a score either better than A’s or worse
> The average income of a group of people is £8000, and 80% of the group have incomes within the range £6000–10 000. What is the minimum value of the standard deviation of the distribution?
> At another stall, you have to toss a coin numerous times. If a head does not appear in 20 tosses you win £1 billion. The entry fee for the game is £100. a. What are your expected winnings? b. Would you play?
> A newspaper advertisement reads ‘The sex of your child predicted, or your money back!’ Discuss this advertisement from the point of view of (a) the advertiser and (b) the client.
> A motorist keeps a record of petrol purchases on a long journey, as follows: Calculate the average petrol price for the journey. Petrol station 1 2 3 Litres purchased 33 40 25 Price per litre (pence) 134 139 137
> Sketch the probability distribution for the likely time of departure of a train. Locate the timetabled departure time on your chart.
> How might you estimate the probability of a corporation reneging on its bond payments?
> The data below show the number of enterprises in the United Kingdom in 2010, arranged according to employment: Number of employees Number of firms 1 ……………………………………………………………. 1 740 685 5 ……………………………………………………………. 388 990 10 ……………………………………………………………. 215
> Sketch the probability distribution for the number of accidents on a stretch of road in one day.
> A train departs every half hour. You arrive at the station at a completely random moment. Sketch the probability distribution of your waiting time. What is your expected waiting time?
> Construct a chain index for 2001–10 using the following data, setting 2004 = 100. 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 87 95 100 105 98 93 100 104 110 100 106 112
> Demonstrate that the weighted average calculation given in equation (1.9) is equivalent to finding the total expenditure on education divided by the total number of pupils.
> The following data show the education and employment status of women aged 20–29: a. Draw a bar chart of the numbers in work in each education category (the first line of the table). Can this be easily compared with the similar diagram
> How does moderate participation differ from complete participation?
> Discuss how ethnography and participant observation are related.
> Define reliability and validity in the context of qualitative research.
> How does narrative analysis differ from content analysis?
> What is grounded theory?
> How can you assess the reliability and validity of qualitative research?
> A production manager wants to assess the reactions of the blue‐collar workers in his department (including foremen) to the introduction of computer‐integrated manufacturing (CIM) systems. He is particularly interested to know how they perceive the effect
> David Shen Liang is a business student engaged in a management project for Ocg Business Services (OBS), a supplier of office equipment to a large group of (international) customers. OBS operates in the Businessto‐business market. David
> Critique Report 3 in the Appendix. Discuss it in terms of good and bad research, suggesting how the study could have been improved, what aspects of it are good, and how scientific it is.
> The following data are available: Note: Maximum exam mark = 100, Maximum paper mark = 100, Sex: M = male, F = female, Year in college: 1 = Freshman; 2 = Sophomore; 3 = Junior; 4 = Senior. 1. Data handling a. Enter the data in SPSS. Save the file to yo
> Dear Respondent, I am final year student studying Business Information Technology (BIT). For my research project I am conducting a survey related to online buying. It would be great if you could answer some questions about this topic. There are no right
> T-Mobile is a mobile network operator headquartered in Bonn, Germany. The company has enlisted your help as a consultant to develop and test a model on the determinants of subscriber churn in the German mobile telephone market. Develop a sampling plan an
> The Executive board of a relatively small university located in Europe wants to determine the attitude of their students toward various aspects of the University. The university, founded in 1928, is a fully accredited government financed university with
> A consultant had administered a questionnaire to some 285 employees using a simple random sampling procedure. As she looked at the responses, she suspected that two questions might not have been clear to the respondents. She would like to know if her sus
> A magazine article suggested that “Consumers 35 to 44 will soon be the nation’s biggest spenders, so advertisers must learn how to appeal to this “over-the-thrill crowd”. If this suggestion appeals to an apparel manufacturer what should be the sampling d
> The medical inspector desires to estimate the overall average monthly occupancy rates of the cancer wards in 80 different hospitals which are evenly located in the Northwestern, Southeastern, Central, and Southern suburbs of New York city.
> Develop an ordinal scale for consumer preferences for different brands of cars.
> Suggest two variables that would be natural candidates for nominal scales, and set up mutually exclusive and collectively exhaustive categories for each.
> The SERVQUAL-scale described in the appendix is formative in nature.” Comment on this statement. Explain why it does not make sense to assess the inter-item consistency of this scale.
> Develop and name the type of measuring instrument you would use to tap the following: a. Which brands of toothpaste are consumed by how many individuals? b. Among the three types of exams – multiple choice, essay type, and a mix of both – which is the o
> Mention one variable for each of the four scales in the context of a market survey, and explain how or why it would fit into the scale.
> Dawson Chambers is a young, dynamic and fast growing research agency that is specialized in Mystery Shopping, Market Research, and Customer Service Training. It is located in Geneva, Switzerland from where it provides national and international organizat
> Measure any three variables on an interval or a ratio scale.
> Design an interview schedule to assess the “intellectual capital” as perceived by employees in an organization – the dimensions and elements for which you developed earlier.
> a. Read the paper by Cacioppo and Petty (1982) and describe how the authors generated the pool of 45 scale items that appeared relevant to need for cognition. b. Why do we need 34 items to measure “need for cognition”? Why do three or four items not suf
> Identify the object and the attribute. Give your informed opinion about who would be an adequate judge. a. Price consciousness of car buyers. b. Self‐esteem of dyslexic children. c. Organizational commitment of school teachers. d. Marketing orientati
> Find the paper “Consumer values orientation for materialism and its measurement: Scale development and validation,” written by Marsha Richins and Scott Dawson. a. Provide an overview of the dimensions and elements of Richins and Dawson’s materialism sca
> Compare your service quality measure to the measure of Zeithaml, Berry, and Parasuraman (1996) presented in the Journal of Retailing. a. How does your measure differ from this measure in terms of dimensions and elements? b. Would you prefer using your
> Try to come up with two unidimensional and two multidimensional abstract concepts. Explain why these concepts have either one or more than one dimension.
> What are projective techniques and how can they be profitably used?
> Explain the possible ways in which you can control “nuisance” variables.
