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Statistics For Economics Accounting And Business Studies 7th Edition Michael Barrow - Solutions

Compare the degrees of concentration in the following two industries. Can you say which is likely to be more competitive? Firm A B CD E F G H Sales 337 384 696 321 769 265 358 521 880 334 Sales 556 899 104 565 782 463 477 846 911 227
Calculate the three-firm concentration ratio for employment in the following industry:Firm A B C D E F G Firm A B C 0 E F G H Employees 3350 290 440 1345 821 112 244 352
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?
The following table shows the income distribution by quintile for the United Kingdom in 2006–7, for various definitions of income:(a) Use equation (10.27) to calculate the Gini coefficient for each of the four categories of income.(b) For the ‘original income’ category, draw a smooth Lorenz
(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 2005 wealth data?
(a) Draw a Lorenz curve and calculate the Gini coefficient for the wealth data in Table 1.3 (Chapter 1).(b) Why is the Gini coefficient typically larger for wealth distributions than for income distributions?
Calculate the internal rates of return for the projects in Problem 10.14.
Calculate the internal rate of return for the project in Problem 10.13. Use either trial and error methods or a computer to solve.
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 2 3 5 6 5600 1000 1400 1500 2100 1450 700 6000 800 1400 1750 2500 1925 1200
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:(In all the following answers, set your index to 1987 = 100.)(a) Turn the expenditure cash figures into an index number
Using the data in Problem 10.6, calculate how much the average consumer would need to be compensated for the rise in prices between 1990 and 1994.
Industry is always concerned about the rising price of energy. It demands to be compensated for any rise over 5% in energy prices between 2007 and 2008. How much would this compensation cost?Which price index should be used to calculate the compensation and what difference would it make? (Use the
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
The following table shows the weights in the retail price index and the values of the index itself, for 1990 and 1994.(a) Calculate the Laspeyres price index for 1994, based on 1990 = 100.(b) Draw a bar chart of the expenditure weights in 1990 and 1994 to show how spending patterns have changed.
(a) Using the data in Problem 10.3, calculate the expenditure shares on each fuel in 1999 and the individual price index number series for each fuel, with 1999 = 100.(b) Use these data to construct the Laspeyres price index using the expenditures shares approach.Check that it gives the same answer
The prices of different house types in south-east England are given in the table below:(a) If the numbers of each type of house in 1991 were 1898, 1600, 1601, 499 and 1702, respectively, calculate the Laspeyres price index for 1991–94, based on 1991 = 100.(b) Calculate the Paasche price index,
The following tables show energy prices and consumption in 1999–2003 (analogous to the data in the chapter for the years 2006–10).(a) Construct a Laspeyres price index using 1999 as the base year.(b) Construct a Paasche price index. Compare this result with the Laspeyres index. Do they differ
The following data show the gross operating surplus of companies, 2005–10, in the United Kingdom, in £m.(a) Turn the data into an index number series with 2005 as the reference year.(b) Transform the series so that 2008 is the reference year.(c) What increase has there been in profits between
The data below show exports and imports for the United Kingdom, 2005–10, in £bn at current prices.(a) Construct index number series for exports and imports, setting the index equal to 100 in 2005 in each case.(b) Is it possible, using only the two indices constructed in part (a), to construct an
(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 (applies to the United Kingdom, other countries will differ) – precise details can be obtained in various guides to usedcar
(Project) Visit your college library or online sources to collect data to answer the following question.Have females’ earnings 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 process,
Find figures for the monetary aggregate M0 for the years 1995 to 2003 in the United Kingdom, in nominal terms.
Find the gross domestic product for both the United Kingdom and the United States for the period 1995 to 2003. Obtain both series in constant prices.
(Project) Build a suitable model to predict car sales in the United Kingdom. You should use time-series data (at least 20 annual observations). You should write a report in a similar manner to Problem 7.12.
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)
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 (.56) (5.9) (2.5) (3.8) (3.2) (3.9)R2 = 0.76, se =
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.
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.
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.
(This problem continues the analysis from Problem 8.2.) Given the following data for a family:(a) Predict the level of alcohol expenditure for this family.(b) If their actual expenditure turned out to be 32.50, how accurate would you judge the prediction? Family Income Adults Smoker 18 700 2 1
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).
The following data show the number of adults in each of 17 households and whether or not the family contains at least one person who smokes, to supplement the data in Problem 7.2 on alcohol spending (see page 301).(a) Estimate a multiple regression model of expenditure on alcohol, using income, the
(a) Using the data in Problem 7.1 (page 301), 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 the
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 problem;data
(Project) Update Todaro’s study using more recent data.
Predict alcohol consumption given an income of £700. Use the 99% confidence level for the interval estimate.
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.
(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?(c) Test the
(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
(a) Calculate the rank correlation coefficient between income and quantity for the data in Problem 7.2. How does it compare to the ordinary correlation coefficient?(b) Is there significant evidence that the ranks are correlated?
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?
As Problem 7.3, for(a) real consumption and real income;(b) individuals’ alcohol and cigarette consumption;(c) UK and US interest rates.
The data below show alcohol expenditure and income (both in £s per week) for a sample of 17 families.(a) Draw an XY plot of the data and comment.(b) From the chart, would you expect the line of best fit to slope up or down? In theory, which way should it slope?(c) What would you expect the
The other data which Todaro might have used to analyse the birth rate were:For one of the three possible explanatory variables (in class, different groups could examine each of the variables):(a) Draw an XY chart of the data above and comment upon the result.(b) Would you expect a line of best fit
(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 x2 test to examine whether there is any bias towards any particular integer. Compare your results with those of others in your class.
(Project) Conduct a survey among fellow students to examine whether there is any association between:(a) gender and political preference, or(b) subject studied and political preference, or(c) star sign and personality (introvert/extrovert – self-assessed: I am told that Aries, Cancer, Capricorn,
An example in Chapter 5 compared R&D expenditure in Britain and Germany. The sample data were:x1 = 3.7 x2 = 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 implications,
Given the following data on two sample variances, test whether there is any significant difference.Use the 1% significance level.s21= 55 s22= 48 n1 = 25 n2 = 30
(a) Do the accountants’ job properly for them (see the Oops! box in the text (page 244)).(b) It might be justifiable to omit the ‘no responses’ entirely from the calculation. What happens if you do this?
A survey of 64 families with five children found the following gender distribution: Number of boys Number of fames 1 2 28 19 Test whether the distribution can be adequately modelled by the Binomial distribution.
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.
Using the data n = 70, s = 15, construct a 99% confidence interval for the true standard deviation.
(Project) This is similar to Problem 5.26 but concerns digital music files. There is debate about whether listeners can tell the difference between high-quality WAV files and compressed MP3 files.Obtain the same song in both formats (most music players will convert a WAV file to MP3) and see if a
(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= RAND(
(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 he or she gets more than p correct, you conclude he or she can tell the
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.Does the introduction of rest days alone appear to improve performance? Before 51 59 51 53 58 58 52 55 61 54 55 After 54 63 55 57 63 63 58 60
The output of a group of 11 workers before and after an improvement in the lighting in their factory is as follows:Test whether there is a significant improvement in performance (a) assuming these are independent samples, (b) assuming they are dependent. Before 52 60 58 58 53 51 52 59 60 53 55
(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
(a) A random sample of 20 observations yielded a mean of 40 and standard deviation 10. Test the hypothesis that m = 45 against the alternative that it is not. Use the 5% significance level.(b) What assumption are you implicitly making in carrying out this test?
(a) 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.(b) If you test whether the group of people who passed the driving test contained the same proportion of men as
Given the following data from two independent samples:x1 = 115 x2 = 105 s1 = 21 s2 = 23 n1 = 49 n2 = 63 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.
Test H0: p = 0.5 against H0: p 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 tyres an improvement? Use the 5%significance
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.
Given the two hypotheses H0: m = 400 H1: m = 415 and s2 = 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 Ú 410 from a sample of size 40, find the probability of a Type II error and the power of the test.(c)
What is the power of the test carried out in Problem 5.3?
Given the sample data x = 45, s = 16, n = 50, at what level of confidence can you reject H0: m = 40 against a two-sided alternative?
Testing the null hypothesis that m = 10 against m 7 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 highdensity 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 diskettes from each batch of 1000 and if any
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 (or not known) and explain why.(a) 5% of his
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
(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.
The heights of 10 men and 15 women were recorded, with the following results: Mon Mean 1735 162 Varlance Women 65 Estimate the true difference between men's and women's heights. Use the 95% confidence level.
Two samples were drawn, each from a Normally distributed population, with the following results:x1 = 45 s1 = 8 n1 = 12 x2 = 52 s2 = 5 n2 = 18 Estimate the difference between the population means, using the 95% confidence level.
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) A sample of 954 adults in early 1987 found that 23% of them held shares. Given a UK adult population of 41 million and assuming a proper random sample was taken, find the 95% confidence interval estimate for the number of shareholders in the United Kingdom.(b) A ‘similar’ survey the
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.
(a) A sample of 200 women from the labour force found an average wage of £26 000 p.a. with standard deviation £3500. A sample of 100 men found an average wage of £28 000 with standard deviation £2500. Estimate the true difference in wages between men and women.(b) A different survey, of men and
Given the sample data x1 = 25 x2 = 22 s1 = 12 s2 = 18 n1 = 80 n2 = 100 estimate the true difference between the means with 95% confidence.
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.
(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 necessary to know the correct average
Given the sample data x = 40 s = 10 n = 36 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?
Following the previous question, prove that the most precise unbiased estimate is obtained by setting w1 = w2 = 12. (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.)
Is the 95% confidence interval (a) twice as wide, (b) more than twice as wide and (c) less than twice as wide, as the 47.5% interval? Explain your reasoning.
(Project) A report in The Guardian newspaper (20 June 2010, http://www.guardian.co.uk/education/2010/jun/20/internet-plagiarism-rising-in-schools) reports ‘Half of university students also prepared to submit essays bought off the internet, according to research.’ According to the article, a
(Project) Using a weekend’s football results from the Premier (or other) League, see if the number of goals per game can be adequately modelled by a Poisson process. First calculate the average number of goals per game for the whole league, and then derive the distribution of goals per game using
(Project) An extremely numerate newsagent (with a spreadsheet program, as you will need) is trying to work out how many copies of a newspaper he should order. The cost to him per copy is 40 pence, which he then sells at £1.20. Sales are distributed Normally with an average daily sale of 250 and
(Computer project) 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 columns, to generate 100
A machine producing electronic circuits has an average failure rate of 15% (they are difficult to make). The cost of making a batch of 500 circuits is £8400 and the good ones sell for £20 each.What is the probability of the firm making a loss on any one batch?
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 accurate is the Normal method, with and without the
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 the sample mean being over £10 500?(c) What is
Ten adults are selected at random from the population and their IQ measured. (Assume a population mean of 100 and standard deviation of 16 as in Problem 3.16.)(a) What is the probability distribution of the sample average IQ?(b) What is the probability that the average IQ of the sample is over
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 the population went to university. Now the
If x N(10, 9), find(a) Pr(x 7 12)(b) Pr(x 6 7)(c) Pr(8 6 x 6 15)(d) Pr(x = 10)
For the standard Normal variable z, find(a) Pr(z 7 1.64)(b) Pr(z 7 0.5)(c) Pr(z 7 -1.5)(d) Pr(-2 6 z 6 1.5)(e) Pr(z = -0.75).For (a) and (d), shade in the relevant areas on the graph you drew for Problem 3.11.
Repeat the previous problem for the values m = 2 and s2 = 3, Use values of x from -2 in to +6 increments of 1.
Using equation (3.5) describing the Normal distribution and setting m = 0 and s2 = 1, graph the distribution for the values x = -2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2.
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?
Sketch the probability distribution for the likely time of departure of a train. Locate the timetabled departure time on your chart.

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