Questions and Answers of Business Statistics Using Excel

A teacher of 40 university students studying the application of Excel within a business context is concerned that students are not taking a group work assignment seriously. This is deemed to be
A researcher has undertaken a sign test with the following results: sum of positive and negative signs are 15 and 4, respectively, with 3 ties. Given that binomial p = 0.5, assess whether there is
A battery manufacturer supplies a range of car batteries to car manufacturers. The 40 Amp-hour battery is manufactured at two manufacturing plants with a stated mean time between charges of 8.3 days
During a national election a national newspaper wanted to assess whether there was a similar voting pattern for a particular party between two towns in the north-east of England. The sample results
Suppose a university sampled 485 of its students to determine whether males and females differed in preference for five courses offered. The question we would like to answer is to confirm whether or
Construct a scatter plot for the data in Table 8.4 and calculate Pearson’s correlation coefficient, r. Comment on the strength of the correlation between x and y. X: y: Table
Samples of students’ essays were marked by two tutors independently. The resulting ranks are shown in Table 8.7.(a) Calculate the rank correlation coefficient.(b) State any conclusions that you can
In the regression equation for ŷ = b0 + b1x, the value of b0 is given by the equation: Α. bo = C. boi ΣΥ-b, ΣΧ n ΣΥ-b, ΣΧ n Β. bo D. bo = ΣΥ-Ε, ΣΧ 20 ΣΥ-ΠΣΧ n
Reconsider the Example 8.1 data set and test the significance of the predictor variable (x).Data from Example 8.1A large manufacturing firm with some 8000 employees has designed a training programme
In 2007 Pronto Ltd ascertained the amount spent on advertising and the corresponding sales revenue by seven marketing clients (Table 8.14).(a) Plot a scatter plot and comment on a possible
Figure 9.6 illustrates the Excel calculation procedure to calculate the required indices for the average annual oil price. EEEEEEEERRIN Example Figure
The time series given in Table 9.2 is seasonal. What would you say is the periodicity of the seasonal component? X > 1 1 Table 9.2 2 3 3 5 4 3 5 1 6 3 لنا 7 5 00 7 9 10 5 3 11 12 13 5 7 ш 9 14
If a time series can be best fitted with the trend whose equation is y = a + bx + cx2, would you say that this is a linear model?
Chart the time series given in Table 9.1 and decide if it is stationary and or seasonal. X y Table 9.1 1 2 2 5 3 6 st 4 6 5 4 6 5 7 7 8 5 9 8 10 9
Coco S. A. is considering diversifying and entering the housing market in the USA. They are only interested in a short-term investment. To help them with the decision and assess the market, their US
Figure 9.7 illustrates the calculation procedure to calculate the average oil price and index values for oil prices. 1 Example 9.5 13 14 SERENA 822233 Figure
Baker Ltd is concerned about the influence on petrol prices on its profit margins. The owner of the company looked at weekly petrol prices (pence per gallon) for London and compiled a time series.
Let’s take the example of oil prices as before. Column B repeats the average annual price of domestic crude oil in $/bbl. These values are given in current dollars, i.e. the value of the dollar in
Is it possible to have a time series that is non-seasonal and non-stationary? If so, how would you call it and can you draw a graph showing how such a series might look?
Skodel Ltd is considering investing into technology stocks. As a test case, it looked at Microsoft-adjusted monthly closing values of stocks between 1 March 2001 and 1 August 2008. The time series is
Using the previously-described technique for converting indices from one base to another, if we wanted to calculate the price of oil on the basis of a constant value of US dollars for the year 2007,
Go to one of the websites that allow you to download financial time series (e.g. http://finance.yahoo.com/) and plot the series of your choice in several identical line graphs. Change the scale of
In this example we will fit a trend line to a time series data set given the value of the slope of the trend line and its intercept. Figure 9.17 illustrates the manual calculation of the trend line
Take the first differences between the observations in the time series from X9.1. Would you say that the differenced time series is stationary? If it is not what would you do to make it
Repeat Example 9.11, but this time use the Excel function INTERCEPT() and SLOPE() to calculate these values in Cells H3 and H4. Figure 9.19 illustrates the change to cells H3 and H4 in the Excel
Calculate indices based on year 2000 for the series shown in Table 9.5. Could you convert them into indices based on year 2003? Year Sales Table
We created another short time series and calculated moving averages in Figure 9.26. A 1 Example 9.15 12345678 8 Period 1 2 3 4 5 C Series 150 250 200 360 300 3MA 200.0 270.0 286.7 SUM(C4:C6y3 SUM(C5
Use the CPI values from Figure 9.8 to convert the sales values from the student exercise X9.6 to a constant dollar value based on the 2004 value of the dollar.Data from Exercises 9.6Calculate indices
Figure 9.31 shows how the moving averages were calculated for a three point moving average (3MA) and the use of the model to provide a forecast at time point 31. 1 Example 9.17 2 34567828858
What is the real value of the sales value in 2007 if you put it on the constant year 2000 basis?
As an example, we can use the same short time series we used to demonstrate how to use moving averages, to create forecasts using Brown’s exponential smoothing method, as illustrated in Figure
If the time series components were extracted as in Table 9.7, how would you reconstruct the time series (ŷ) using:(a) An additive model (b) A mixed model? T C I a Table
Consider the data set in Table 9.9 and smooth the data using Brown’s exponential smoothing method with smoothing factors 0.1 and 0.9. Time point 1 2 3 4 5 6 7 00 9 10 Table 9.9 Series
In this example we will show how to use all the formulae listed in this chapter and we will demonstrate how to use the Data Analysis > Exponential Smoothing to undertake the analysis. Figures 9.40
R-squared (R2) is a measure of how closely a trend fits the time series. What is another expression for this statistic and in what context have we used it when discussing linear regression?
For the time series data presented in Table 9.10 calculate seasonal forecasts using the simple seasonal additive exponential smoothing model.If we plot the time series as illustrated in Figure 9.44
Does R2 = 0.90 indicate a good fit? Why?
Extrapolate the time series in Table 9.8 three time periods in the future. Use the TREND function. Why do you think it would not make sense to extrapolate this time series 10 time periods in the
For what kind of time series would you use a multiplicative versus additive seasonal exponential smoothing model?
Why are seasonal parameters at and St in the seasonal exponential smoothing method called dynamic parameters?
What is the role of mean square error (MSE) in seasonal exponential smoothing method?
Why is the MAD type of error measurement preferred over the ME type of error?
Two forecasts were produced, as shown in Table 9.11. The ME for the second forecast is some seven times larger than the ME for the first forecast. However, the MSE is some 20 times larger. Can you
It is acceptable to see some regularity in pattern when examining the series of residuals or forecasting errors?
The closer the actual observations, when compared with forecasted values on a scatter diagram, are to the diagonal line, the better the forecasts. Is this correct?
How would you describe the concept of confidence interval in the context of precision in forecasting?
Would you use the z-values or t-values to calculate the confidence interval for a time series that has 200 observations?
Why is it logical to expect that the confidence interval should get wider and wider the further we go in the future with our forecasts?
In the course of a survey relating to examination success, you have discovered a high negative correlation between students’ hours of study and their examination marks. This is so at variance with
Coco S. A. has requested that a local property company undertake an analysis of property prices. The initial data collection has been undertaken and independent variables identified: square feet,
Bakers Ltd is concerned at the possible relationship between the amount of fat (grams) and the number of calories in a popular pie (Table 8.22).(a) Plot a scatter plot and comment on a possible
Reconsider the data set in Example 8.1.Data from Example 8.1A large manufacturing firm with some 8000 employees has designed a training programme that is supposed to increase the production of
Display the data given in Table 8.5 in an appropriate form and state how the variables are correlated. X: y: Table 8.5 0 806 15 630 30 643 45 625 60 575 75 592 90 408 105 469 120 376
Skodel Ltd employs a local transport company to deliver beers to local supermarkets. To develop better work schedules, the managers want to estimate the total daily travel time for their drivers’
Table 8.6 indicates the number of vehicles and number of road deaths in ten countries.(a) Construct a scatter plot and comment upon the possible relationship between the two variables.(b) Calculate
The mathematics and statistics examination marks for a group of ten students are shown in Table 8.8.(a) Find the correlation coefficient for the two sets of marks.(b) Place the marks in rank order
You are asked to decide whether the statistics rank correlates with the mathematics rank for seven students provided in Table 8.2. As the information is ranked we use Spearman’s correlation
Three people, P, Q, and R, were asked to place in preference nine features of a house (A, B, C ... I). Calculate Spearman’s rank order correlation coefficients between the pairs of preferences, as
Reconsider the data set in Example 8.6 and assess the significance of rs.Data from Example 8.6.You are asked to decide whether the statistics rank correlates with the mathematics rank for seven
In the regression equation for ŷ = b0 + b1x, the value of b1 is given by the equation: A. bi Cb = = ηΣΧΥ – ΣΧΣΥ η Σχ? – (ΣΧ) ΠΣΧΥ – ΣΧΣΥ ΠΣΧ - (ΣΧ) B.
Calculate the coefficient of determination (COD):A. 0.78 B. 1.80 C. 0.80 D. 1.80
Use the Excel TREND() function to fit a trend line to the Example 8.1 data set, as illustrated in Figure 8.20.Data from Example 8.1A large manufacturing firm with some 8000 employees has designed a
Calculate the value of Pearson’s correlation coefficient (r):A. 0.99 B. 1.89 C. 0.11 D. 0.89
Reconsider the data set in Example 8.1 and test the linear regression model reliability.Data from Example 8.1A large manufacturing firm with some 8000 employees has designed a training programme that
Calculate the value of the standard estimate of the error (SEE):A. 84078 B. 84778 C. 48078 D. 48178
Reconsider the data in Example 8.1 and conduct an F test to test whether or not the dependent variable is a significant contributor to the dependent variable.Data from Example 8.1A large
Fit an appropriate equation to the data set (Table 8.15) to predict the examination mark given the assignment mark for 14 undergraduate students.(a) Plot a scatter plot and comment on a possible
Reconsider Example 8.1 and calculate a 95% confidence interval for the slope coefficient of the predictor variable.Data from Example 8.1A large manufacturing firm with some 8000 employees has
Fit a prediction interval at xp = 30 to the data set from Example 8.1.Data from Example 8.1A large manufacturing firm with some 8000 employees has designed a training programme that is supposed to
Table 8.18 consists of data that has been collected by an estate agent who wishes to model the relationship between house sales price (£) and the independent variables: land value, LV (£) and the
CoCo S.A. is concerned about the time taken to react to customer complaints and has implemented a new set of procedures for its support centre staff . The customer service director has decided that
A business consultant requests that you perform some preliminary calculations before analysing a data set using Excel.(a) Calculate the number of degrees of freedom for a contingency table with three
Bakers Ltd are currently undertaking a review of the delivery vans used to deliver products to customers. The company runs two types of delivery van (type A, recently purchased, and type B, at least
To illustrate the concept consider the example of a firm who surveys whether or not employees use the train to travel to work. The firm collects the data and has created a 2 * 2 contingency table
A trainee risk manager for an investment bank has been told that the level of risk is related directly to the industry type (manufacturing, retail, and fi nancial). For the data presented in the
Skodel Ltd is developing a low calorie lager for the European market with a mean designed calorie count of 43 calories per 100 ml. The new product development team are having problems with the
A manufacturing company is concerned at the number of defects produced by the manufacture of office furniture. The firm operates three shifts and has classified the number of defects as low,
To illustrate the method consider the example of a motorway safety officer who believes that the number of accidents per week occurring on a stretch of motorway can be modelled using a Poisson
A local trade association is concerned at the level of business activity within the local region. As part of a research project a random sample of business owners were surveyed on how optimistic they
To illustrate the concept consider the situation where 16 randomly-selected people were chosen to measure the effectiveness of a new training programme on the value of sales. For the training
A group of students at a language school volunteered to sit a test that is to be undertaken to assess the effectiveness of a new method to teach German to English-speaking students. To assess
A business analyst requests answers to the following questions:(a) What is the p-value when the chi-square test statistic = 2.89 and we have one degree of freedom?(b) If you have one degree of
A local training firm has developed an innovative programme to improve the performance of students on the courses it offers. To assess whether the new programme improves student performance the firm
The petrol prices during the summer of 2008 raised concerns with new car sellers that potential customers were taking prices into account when choosing a new car. To provide evidence to test this
A business analyst has been asked to confirm the effectiveness of a marketing campaign on people’s attitudes to global warming. To confirm that the campaign was effective a group of 500 people were
An employment agency has recently implemented a new training programme to develop the interview skills of potential job applicants. Based upon the collected data (Table 7.14) can we say confidently
A university has recently set up a satellite department within a local college of higher education. The university claims that 35% of the undergraduate students are in department A, 26% are in
A new airport terminal has been assessing waiting times for passengers to be processed at the airport check-in counters. The airport owners would like to be able to attach levels of risk to diff
A leading business-training firm advertises in its promotional material that its class sizes at its Paris branch are no greater than 25. Recently, the firm has received a number of complaints from
The Wilcoxon paired ranks test is considered to be more powerful than the sign test. Explain why.
A company is planning to introduce new packaging for a product that has used the same packing for over 20 years. Before it makes a decision on the new packaging it decides to ask a panel of 20
A local manufacturer is concerned at the number of errors made by machinists in the production of kites for a multinational retail company. To reduce the number of errors being made the company
What assumptions need to be made about the type and distribution of the data when the Mann–Whitney test is used?
Two groups of randomly-selected students are tested on a regular basis as part of professional appraisals that are conducted on a two-year cycle by a leading financial services company based in
The sale of new homes is tied closely to the level of confidence within the financial markets. A developer builds new homes in two European countries (A and B) and is concerned that there is a direct
The Indian restaurant manager has employed two new delivery drivers and wishes to assess their performance. The data in Table 6.3 represent the delivery times for person A and B undertaken on the
In this example we will use the F test to check if the two population variances in Example 6.7 can be considered equal with a 95% confidence.Data from Example 6.7A certain product of organic beans
Reconsider Example 6.13, but use the Data Analysis tool to undertake the analysis.Data from Example 6.13In this example we will use the F test to check if the two population variances in Example 6.7
A national airline keeps a record of luggage misplaced at two European airports during one week in the summer of 2006. The sample results are illustrated in Table 6.5Assess whether there is a
Let us illustrate the calculation of the type II error (β) and the statistical power via a simple example. Consider the problem of estimating the spend on a particular type of sweet per day where,

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