Statistics For Economics Accounting And Business Studies 5th Edition Mr Michael Barrow - Solutions

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f#!# 11.9 Project: Obtain quarterly (unadjusted!) data for a suitable variable (some suggestions are given below) and examine its seasonal pattern. Write a brief report on your findings. You should: (a) Say what you expect to find, and why. (b) Compare different methods of adjustment. (c) Use your
11.8 (a) How many seasonal dummy variables would be needed for the regression approach to the data in Problem 11.3? (b) Do you think the approach would bring as reliable results as it did for consumers’ expenditure?
11.7 A computer will be needed to solve this and the next Problem. (a) Repeat the regression equation from Problem 11.5 but add three seasonal dummy variables (for quarters 2, 3 and 4) to the regressors. (The dummy for quarter 2 takes the value 1 in Q2, 0 in the other quarters. The Q3 dummy takes
11.6 (a) Using the data from Problem 11.3 (2004–2006 only), fit a linear regression line to obtain the trend values. By how much, on average, does car production increase per year? (b) Calculate the seasonal factors (multiplicative model). How do they compare to the values in Problem 11.3? (c)
11.5 (a) Using the data of Problem 11.1, fit a regression line through the data, using t and t 2 as explanatory variables (t is a time trend 1–36). Use only the observations from 2000–2006. Calculate the trend values using the regression. (b) Calculate the seasonal factors (multiplicative
11.4 Repeat Problem 11.3 using the additive model and compare results.
11.3 The following data relate to car production in the UK (not seasonally adjusted). 2003 2004 2005 2006 2007 January – 141.3 136 119.1 124.2 February – 141.1 143.5 131.2 115.6 March – 163 153.3 159 138 April – 129.6 139.8 118.6 120.4 May – 143.1 132 132.3 127.4 June – 155.5 144.3
11.2 Repeat the exercise using the additive model. (In Problem 11.1(c) above, subtract the moving average figures from the original series. In (e), subtract the seasonal factors from the original data to get the adjusted series.) Is there a big difference between this and the multiplicative model?
11.1 The following table contains data for consumers’ non-durables expenditure in the UK, in constant 2003 prices. Q1 Q2 Q3 Q4 1999 – – 153 888 160 187 2000 152 684 155 977 160 564 164 437 2001 156 325 160 069 165 651 171 281 2002 161 733 167 128 171 224 176 748 2003 165 903 172 040 176 448
10.23 (Project) The World Development Report contains data on the income distributions of many countries around the world (by quintile). Use these data to compare income distributions across countries, focusing particularly on the differences between poor countries, middle-income and rich
10.22 Compare the degrees of concentration in the following two industries. Can you say which is likely to be more competitive? Firm A B C D E F G H I J Sales 337 384 696 321 769 265 358 521 880 334 Sales 556 899 104 565 782 463 477 846 911 227
10.21 Calculate the three-firm concentration ratio for employment in the following industry: Firm A B C D E F G H Employees 3350 290 440 1345 821 112 244 352
10.20 For the Kravis, Heston and Summers data (Table 10.26), combine the deciles into quintiles and calculate the Gini coefficient from the quintile data. How does your answer compare with the answer given in the text, based on deciles? What do you conclude about the degree of bias?
10.19 The following table shows the income distribution by quintile for the UK in 2006–2007, for various definitions of income: Quintile Income measure Original Gross Disposable Post-tax 1 (bottom) 3% 7% 7% 6% 2 7% 10% 12% 11% 3 15% 16% 16% 16% 4 24% 23% 22% 2% 5 (top) 51% 44% 42% 44% (a) Use
10.18 (a) Draw a Lorenz curve and calculate the Gini coefficient for the 1979 wealth data contained in Problem 1.5 (Chapter 1). Draw the Lorenz curve on the same diagram as you used in Problem 10.17. (b) How does the answer compare to 2003?
10.17 (a) Draw a Lorenz curve and calculate the Gini coefficient for the wealth data in Chapter 1 (Table 1.3). (b) Why is the Gini coefficient typically larger for wealth distributions than for income distributions?
10.16 Calculate the internal rates of return for the projects in Problem 10.14.
10.15 Calculate the internal rate of return for the project in Problem 10.13. Use either trial and error methods or a computer to solve.
10.14 A firm uses a discount rate of 12% for all its investment projects. Faced with the following choice of projects, which yields the higher NPV? Project Outlay Income stream 123456 A 5600 1000 1400 1500 2100 1450 700 B 6000 800 1400 1750 2500 1925 1200
10.13 A firm is investing in a project and wishes to receive a rate of return of at least 15% on it. The stream of net income is: Year 1234 Income 600 650 700 400 (a) What is the present value of this income stream? (b) If the investment costs £1600 should the firm invest? What is the net present
10.12 (a) If w represents the wage rate and p the price level, what is w/p? (b) If Δw represents the annual growth in wages and i is the inflation rate, what is Δw − i? (c) What does ln(w) − ln(p) represent? (ln = natural logarithm)
10.11 The following data show expenditure on the National Health Service (in cash terms), the GDP deflator, the NHS pay and prices index, population and population of working age: Year NHS GDP NHS pay and Population Population of expenditure deflator price index (000) working age (£m) 1973 = 100
10.10 Using the data in Problem 10.6 above, calculate how much the average consumer would need to be compensated for the rise in prices between 1990 and 1994.
10.9 Industry is complaining about the rising price of energy. It demands to be compensated for any rise over 5% in energy prices between 2003 and 2004. How much would this compensation cost? Which price index should be used to calculate the compensation and what difference would it make? (Use the
10.8 Construct a chain index for 1995–2004 using the following data, setting 1998 = 100. 1995 1996 1997 1998 2002 2000 2001 2002 2006 2004 87 95 100 105 98 93 100 104 110 100 106 112
10.7 Construct a chain index from the following data series: 1998 2002 2000 2001 2002 2006 2004 Series 1 100 110 115 122 125 Series 2 100 107 111 119 121 What problems arise in devising such an index and how do you deal with them?
10.6 The following table shows the weights in the retail price index and the values of the index itself, for 1990 and 1994. Food Alcohol Housing Fuel Household Clothing Personal Travel Leisure and and items goods tobacco light Weights 1990 205 111 185 50 111 69 39 152 78 1994 187 111 158 45 123 58
10.5 (a) Using the data in Problem 10.3, calculate the expenditure shares on each fuel in 1995 and the individual price index number series for each fuel, with 1995 = 100. (b) Use these data to construct the Laspeyres price index using the expenditures shares approach. Check that it gives the same
10.4 The prices of different house types in south-east England are given in the table below: Year Terraced houses Semi-detached Detached Bungalows Flats 1991 59 844 77 791 142 630 89 100 47 676 1992 55 769 73 839 137 053 82 109 43 695 1993 55 571 71 208 129 414 82 734 42 746 1994 57 296 71 850 130
10.3 The following data show energy prices and consumption in 1995–1999 (analogous to the data in the chapter for the years 2002–2006). Prices Coal (£/tonne) Petroleum (£/tonne) Electricity (£/MWh) Gas (£/therm) 1995 37.27 92.93 40.07 0.677 1996 35.41 98.33 39.16 0.464 1997 34.42 90.86
10.2 The following data show the gross trading profits of companies, 1987–1992, in the UK, in £m. 1987 1988 1989 1990 1991 1992 61 750 69 180 73 892 74 405 78 063 77 959 (a) Turn the data into an index number series with 1987 as the reference year. (b) Transform the series so that 1990 is the
10.1 The data below show exports and imports for the UK, 1987–1992, in £bn at current prices. 1987 1988 1989 1990 1991 1992 Exports 120.6 121.2 126.8 133.3 132.1 135.5 Imports 122.1 137.4 147.6 148.3 140.2 148.3 (a) Construct index number series for exports and imports, setting the index equal
9.8 (Project) Do a survey to find the average age of cars parked on your college campus. (A letter or digit denoting the registration year can be found on the number plate – precise details can be obtained in various guides to used-car prices.) You might need stratified sampling (e.g. if
9.7 (Project) Visit your college library or online sources to collect data to answer the following question. Has women’s remuneration risen relative to men’s over the past 10 years? You should write a short report on your findings. This should include a section describing the data collection
9.6 A firm has £10 000 to spend on a survey. It wishes to know the average expenditure on gas by businesses to within £30 with 99% confidence. The variance of expenditure is believed to be about 40 000. The survey costs £7000 to set up and then £15 to survey each firm. Can the firm achieve its
9.5 A firm wishes to know the average weekly expenditure on food by households to within £2, with 95% confidence. If the variance of food expenditure is thought to be about 400, what sample size does the firm need to achieve its aim?
9.4 Find figures for the monetary aggregate M0 for the years 1995–2003 in the UK, in nominal terms.
9.3 Find the gross domestic product for both the UK and the US for the period 1995–2003. Obtain both series in constant prices.
9.1 What issues of definition arise in trying to measure ‘output’? 9.2 What issues of definition arise in trying to measure ‘unemployment’?
8.13 (Project) Build a suitable model to predict car sales in the UK. You should use time-series data (at least 20 annual observations). You should write a report in a similar manner to Problem 7.12 (see page 275).
8.12 In a cross-section study of the determinants of economic growth (National Bureau of Economic Research, Macroeconomic Annual, 1991), Stanley Fischer obtained the following regression equation GY = 1.38 − 0.52RGDP70 + 2.51PRIM70 + 11.16INV − 4.75INF + 0.17SUR (−5.9) (2.69) (3.91) (2.7)
8.11 R. Dornbusch and S. Fischer (in R. E. Caves and L. B. Krause, Britain’s Economic Performance, Brookings, 1980) report the following equation for predicting the UK balance of payments B = 0.29 + 0.24U + 0.17 ln Y − 0.004t − 0.10 ln P − 0.24 ln C t (0.56) (5.9) (2.5) (3.8) (3.2) (3.9) R2
8.10 As Problem 8.9, for: (a) investment; (b) the pattern of UK exports (i.e. which countries they go to); (c) attendance at football matches.
8.9 How would you estimate a model explaining the following variables? (a) airline efficiency; (b) infant mortality; (c) bank profits. You should consider such issues as whether to use time-series or cross-section data; the explanatory variables to use and any measurement problems; any relevant
8.8 As Problem 8.7, for: (a) measurement of economies of scale in the production of books; (b) the determinants of cinema attendances; (c) the determinants of the consumption of perfume.
8.7 Would it be better to use time-series or cross-section data in the following models? (a) the relationship between the exchange rate and the money supply, (b) the determinants of divorce, (c) the determinants of hospital costs. Explain your reasoning.
8.6 As Problem 8.5, for: (a) the output of a car firm, in a production function equation; (b) potential trade union influence in wage bargaining; (c) the performance of a school;
8.4 Given the following data for 1989 and 1990: Year Price of margarine Price of butter Real income 1989 79.3 104.3 120.2 1990 79.3 97.0 122.7 (a) Predict the levels of margarine consumption in the two years. (b) The actual values of consumption for the two years were 3.47 and 3.19. How accurate
8.3 Using the results from Problem 8.1 forecast the birth rate of a country with the following characteristics: GNP equal to $3000, a growth rate of 3% p.a. and an income ratio of 7. (Construct the point estimate only.)
8.2 The following data show the real price of butter and real incomes, to supplement the data in Problem 7.2 (see page 274). Year Price of butter Real income Year Price of butter Real income 1970 105.5 70.3 1980 119.2 92.1 1971 130.9 71.1 1981 114.2 91.4 1972 131.9 77.1 1982 114.5 90.9 1973 99.5
8.1 (a) Using the data in Problem 7.1 (page 273), estimate a multiple regression model of the birth rate explained by GNP, the growth rate and the income ratio. Comment upon: (i) the sizes and signs of the coefficients; (ii) the significance of the coefficients; (iii) the overall significance of
7.12 Try to build a model of the determinants of infant mortality. You should use cross-section data for 20 countries or more and should include both developing and developed countries in the sample. Write up your findings in a report which includes the following sections: discussion of the
7.11 (Project) Update Todaro’s study using more recent data.
7.10 Predict margarine consumption given a price of 70. Use the 99% confidence level.
7.9 From your results for the birth rate model, predict the birth rate for a country with either (a) GNP equal to $3000, (b) a growth rate of 3% p.a. or (c) an income ratio of 7. How does your prediction compare with one using Todaro’s results? Comment.
7.8 (a) For the data given in Problem 7.2, estimate the sample regression line and calculate the R2 statistic. Comment upon the results. (b) Calculate the standard error of the estimate and the standard errors of the coefficients. Is the slope coefficient significantly different from zero? Is
7.7 (a) For the data in Problem 7.1, find the estimated regression line and calculate the R2 statistic. Comment upon the result. How does it compare with Todaro’s findings? (b) Calculate the standard error of the estimate and the standard errors of the coefficients. Is the slope coefficient
7.6 Calculate the rank correlation coefficient between price and quantity for the data in Problem 7.2. How does it compare with the ordinary correlation coefficient?
7.5 Using the data from Problem 7.1, calculate the rank correlation coefficient between the variables and test its significance. How does it compare with the ordinary correlation coefficient?
7.4 As Problem 7.3, for: (a) real consumption and real income; (b) individuals’ alcohol and cigarette consumption; (c) UK and US interest rates.
7.3 What would you expect to be the correlation coefficient between the following variables? Should the variables be measured contemporaneously or might there be a lag in the effect of one upon the other? (a) Nominal consumption and nominal income. (b) GDP and the imports/GDP ratio. (c) Investment
7.2 The data below show consumption of margarine (in ounces per person per week) and its real price, for the UK. Year Consumption Price Year Consumption Price 1970 2.86 125.6 1980 3.83 104.2 1971 3.15 132.9 1981 4.11 95.5 1972 3.52 126.0 1982 4.33 88.1 1973 3.03 119.6 1983 4.08 88.9 1974 2.60 138.8
7.1 The other data which Todaro might have used to analyse the birth rate were: Country Birth rate GNP Growth Income ratio Bangladesh 47 140 0.3 2.3 Tanzania 47 280 1.9 3.2 Sierra Leone 46 320 0.4 3.3 Sudan 47 380 −0.3 3.9 Kenya 55 420 2.9 6.8 Indonesia 35 530 4.1 3.4 Panama 30 1910 3.1 8.6 Chile
6.16 (Computer project) Use your spreadsheet or other computer program to generate 100 random integers in the range 0 to 9. Draw up a frequency table and use a χ2 test to examine whether there is any bias towards any particular integer. Compare your results with those of others in your class.
6.15 (Project) Conduct a survey among fellow students to examine whether there is any association between (a) gender and political preference; (b) subject studied and political preference; (c) star sign and personality (introvert/extrovert – self-assessed: I am told that Aries, Cancer, Capricorn,
6.14 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: Supermarkets 355 251 408 302 Small shops 288 257 225 299 Kiosks 155 352 240 Does the evidence indicate a significant
6.13 Groups of children from four different classes in a school were randomly selected and sat a test, with the following test scores: Class Pupil 1234 567 A 42 63 73 55 66 48 59 B 39 47 47 61 44 50 52 C 71 65 33 49 61 D 49 51 62 48 63 54 (a) Test whether there is any difference between the
6.12 An example in Chapter 4 compared R&D expenditure in Britain and Germany. The sample data were e1 = 3.7 e2 = 4.2 s1 = 0.6 s2 = 0.9 n1 = 20 n2 = 15 Is there evidence, at the 5% significance level, of difference in the variances of R&D expenditure between the two countries? What are the
6.10 A roadside survey of the roadworthiness of vehicles obtained the following results: Roadworthy Not roadworthy Private cars 114 30 Company cars 84 24 Vans 36 12 Lorries 44 20 Buses 36 12 Is there any association between the type of vehicle and the likelihood of it being unfit for the road? 6.11
6.9 (a) Do the accountants’ job properly for them (see the Oops! box in the text (page 218)). (b) It might be justifiable to omit the ‘no responses’ entirely from the calculation. What happens if you do this?
6.8 The following data show the percentages of firms using computers in different aspects of their business: Firm size Computers used in Total numbers of firms Admin. Design Manufacture Small 60% 24% 20% 450 Medium 65% 30% 28% 140 Large 90% 44% 50% 45 Is there an association between the size of
6.7 A survey of 100 firms found the following evidence regarding profitability and market share:Profitability Market share 30% Low 18 7 8 Medium 13 11 8 High 8 12 15 Is there evidence that market share and profitability are associated?
6.6 A company wishes to see whether there are any differences between its departments in staff turnover. Looking at their records for the past year the company finds the following data: Department Personnel Marketing Admin. Accounts Number in post at start of year 23 16 108 57 Number leaving 3 4 20
6.5 Four different holiday firms which all carried equal numbers of holidaymakers reported the following numbers who expressed satisfaction with their holiday: Firm A B C D Number satisfied 576 558 580 546 Is there any significant difference between the firms? If told that the four firms carried
6.4 A survey of 64 families with five children found the following gender distribution: Number of boys 0 1 2 3 4 5 Number of families 1 8 28 19 4 4 Test whether the distribution can be adequately modelled by the Binomial distribution.
6.3 Use the data in Table 6.3 to see if there is a significant difference between road casualties in quarters I and III on the one hand and quarters II and IV on the other.
6.2 Using the data n = 70, s = 15, construct a 99% confidence interval for the true standard deviation.
6.1 A sample of 40 observations has a standard deviation of 20. Estimate the 95% confidence interval for the standard deviation of the population.
5.27 (Computer project) Use the = RAND( ) function in your spreadsheet to create 100 samples of size 25 (which are effectively all from the same population). Compute the mean and standard deviation of each sample. Calculate the z score for each sample, using a hypothesised mean of 0.5 (since the =
5.26 (Project) Can your class tell the difference between tap water and bottled water? Set up an experiment as follows: fill r glasses with tap water and n − r glasses with bottled water. The subject has to guess which is which. If they get more than p correct, you conclude they can tell the
5.25 Discuss in general terms how you might ‘test’ the following: (a) astrology; (b) extra-sensory perception; (c) the proposition that company takeovers increase profits.
5.24 Another group of workers were tested at the same times as those in Problem 5.23, although their department also introduced rest breaks into the working day. Before 51 59 51 53 58 58 52 55 61 54 55 After 54 63 55 57 63 63 58 60 66 57 59 Does the introduction of rest days alone appear to improve
5.23 The output of a group of 11 workers before and after an improvement in the lighting in their factory is as follows: Before 52 60 58 58 53 51 52 59 60 53 55 After 56 62 63 50 55 56 55 59 61 58 56 Test whether there is a significant improvement in performance (a) assuming these are independent
5.22 (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 standard deviation 26 hours. Test whether
5.21 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.
5.20 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?
5.17 A random sample of 180 men who took the driving test found that 103 passed. A similar sample of 225 women found that 105 passed. Test whether pass rates are the same for men and women. 5.18 (a) A pharmaceutical company testing a new type of pain reliever administered the drug to 30 volunteers
5.12 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. Are the new tyres an improvement? Use the 5% significance level. 5.13 Test H0: π =
5.11 Given the following sample data X = 15 s2 = 270 n = 30 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.
5.9 What is the power of the test carried out in Problem 5.3? 5.10 Given the two hypotheses H0: μ = 400 H1: μ = 415 and σ2 = 1000 (for both hypotheses): (a) Draw the distribution of X under both hypotheses. (b) If the decision rule is chosen to be: reject H0 if X 410 from a sample of size 40,
5.8 Given the sample data X = 45, s = 16, n = 50, at what level of confidence can you reject H0: μ = 40 against a two-sided alternative?
5.7 Testing the null hypothesis that μ = 10 against μ > 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.
5.6 Computer diskettes, which do not meet the quality required for high-density (1.44 Mb) diskettes, are sold as double-density diskettes (720 kb) for 80p each. High-density diskettes are sold for £1.20 each. A firm samples 30 diskettes from each batch of 1000 and if any fail the quality test the
5.5 A firm receives components from a supplier, which it uses in its own production. The components are delivered in batches of 2000. The supplier claims that there are only 1% defective components on average from its production. However, production occasionally becomes out of control and a batch
5.4 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?
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, otherwise you will presume it is fair. Write down the null and alternative hypotheses and calculate the probabilities of
5.2 Consider the investor in the text, seeking out companies with weekly turnover of at least £5000. He 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 (or not known) and explain why. (a) 5% of his
5.1 Answer true or false, with reasons if necessary. (a) There is no way of reducing the probability of a Type I error without simultaneously increasing the probability of a Type II error. (b) The probability of a Type I error is associated with an area under the distribution of X assuming the null
4.19 (Project) Estimate the average weekly expenditure upon alcohol by students. Ask a (reasonably) random sample of your fellow students for their weekly expenditure on alcohol. From this, calculate the 95% confidence interval estimate of such spending by all students.
4.18 The heights of 10 men and 15 women were recorded, with the following results: Mean Variance Men 173.5 80 Women 162 65 Estimate the true difference between men’s and women’s heights. Use the 95% confidence level.

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Statistics For Economics Accounting And Business Studies 5th Edition Mr Michael Barrow - Solutions

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