Questions and Answers of Business Statistics Using Excel

During an examination board concerns were raised concerning the marks obtained by students sitting the final year advanced economics (AE) and e-Marketing (EM) papers (Table 6.6).Historically, the
A university finance department would like to compare the travel expenses claimed by staff attending conferences. After initial data analysis the finance director has identified two departments who
Repeat Exercise X6.15, but do not assume equal variances. Are the two sets of results significantly different (test at 5%)?Data from Exercises 6.15During an examination board concerns were raised
Repeat Exercise X6.16, but do not assume equal variances. Are the expenses claimed by department A significantly different to department B?Data from Exercises 6.16A university finance department
Choko Ltd provides training to its salespeople to aid the ability of each salesperson to increase the value of their sales. During the last training session 15 salespeople attended, and their weekly
Concern has been raised at the standard achieved by students completing final year project reports within a university department. One of the factors identified as important is the research methods
In Exercise X6.15 we assumed that the two population variances are equal. Conduct an appropriate test to check if the variances are equal (test at 5% and 1%).Data from Exercises 6.15During an
In Exercise X6.16 we assumed that the two population variances are equal. Conduct an appropriate test to check if the variances are equal (test at 5%).Data from Exercises 6.16A university finance
Generate a random sample of 100 observations from a normal distribution with a mean of 10 and a standard deviation of 4. Calculate the sample mean and standard deviation. Why are these values
A local authority installs 2000 electric lamps. The life of lamps in hours (X) follows a normal distribution, where X ~ N (1000, 40,000). Calculate: (a) The number of lamps that might be expected to
Use the NORM.S.DIST () function to calculate the following probabilities, X ~ N(100, 25): (a) P(X ≤ 95); (b) P(95 ≤ X ≤ 105);(c) P(105 ≤ X ≤ 115); (d) P(93 ≤ X ≤ 99). In each case
Calculate the probability that X lies between 85 and 105 cm for the problem outlined in Example 4.1.In this example we are required to calculate P (85 ≤ X ≤ 105) which represents the area shaded
CoCo S. A. is concerned at the time taken to react to customer complaints and have implemented a new set of procedures for its support centre staff . The customer service director plans to reduce the
Consider two events, A and B, where the associated probabilities are as follows:P(A or B) = 3/4, P(B) = 3/8 and n(A) = 4. Calculate P(A and B) if the total sample size is eight.
Consider Table 3.3 in X3.7.(a) Are the events E and J mutually exclusive?(b) Determine P(E and J).(c) Using the values of P(E), P( J), and P(E and J) you have already determined in X3.7, evaluate
A bag contains three red and four white balls.If one ball is taken at random and then replaced, and another ball is taken calculate the following probabilities:(a) P(first ball red and second ball
Consider two events A and B which contain all sample points with P(A and B) = 1/4 and P(A/B) = 1/3. Calculate (a) P(B), (b) P(A), (c) P(B/A).
In a debate on the alteration of a traffic system in the city centre, measurements of the number of cars per minute were taken at two junctions; the results were as shown in Table 2.19.Compare the
In a number of towns the distance of 1 sample of 122 supermarkets from the towns’ high street was measured to the nearest metre (Table 2.18).Determine the range, mean, and standard deviation.
Obtain a scatter plot for the data in Table 1.37 that represents the passenger miles flown by a UK-based airline (millions of passenger miles) during the period 2003–2004.Comment on the
Obtain a scatter plot for the data in Table 1.36 and comment on whether there is a link between road deaths and the number of vehicles on the road. Would you expect this to be true? Provide reasons
Create a frequency polygon (line graph) for the data in Table 1.32 Age, years 16-17 18-20 21-24 25-29 30-34 35-39 40-44 45-54 55 and over Table 1.32 Frequency, 1000s 4 73 185 104 34 33 22 10 26
Create a suitable histogram to represent the spending on extracurricular activities for a random sample of university students during the ninth week of the first term (Table 1.27).
Create a suitable histogram to represent the number of customers visited by a sales man over an 80-week period (Table 1.26). 68 71 82 83 88 5459757 78 75 85 84 7952 西刀75 64 71 Table 1.26 94 82 68
The results of the voting in an election are shown in Table 1.20.Represent this information on a pie chart. Mr P Mr Q Mrs R Ms S Table 1.20 2045 votes 4238 votes 8605 votes 12,012 votes
Three thousand six hundred people who work in Bradford were asked about the means of transport that they used for daily commuting. The data collected is shown in Table 1.19.Construct a pie chart to
Draw a suitable bar chart for the data in Table 1.16. Industrial sources for consumption and investment demand (thousand million) Producing industry Agriculture, mining Metal manufacturers Other
Table 1.14 represents the number of customers visited by a salesman over an 80-week periodUse Excel to construct a grouped frequency distribution from the data set in Table 1.14 and indicate both
Criticize Table 1.13. Castings Up to 4 ton Up to 10 ton All other weights Other Total Table 1.13 Weight of metal 60 100 110 20 290 Foundry 210 640 800 85 2000
Consider the set of data that represents the number of insurance claims processed each day by an insurance fi rm over a period of 40 days: 3, 5, 9, 6, 4, 7, 8, 6, 2, 5, 10, 1, 6, 3, 6, 5, 4, 7, 8, 4,
Coco S.A. supplies a range of computer hardware and software to 2000 schools within a large municipal region of Germany. When Coco S.A. won the contract the issue of customer service was considered
Bakers Ltd run a chain of bakery shops and is famous for the quality of its pies. The management of the company is concerned at the number of complaints from customers who say it takes too long to
Skodel Ltd is a small brewery that is undergoing a major expansion after a takeover by a large European brewery chain. Skodel Ltd produces a range of beers and lagers, and is renowned for the
Reconsider Example 2.1 to calculate the twenty-fifth percentile and quartile values.Data from Example 2.1Suppose the marks obtained in the statistics examination are as illustrated in Table 2.1.We
Coco S.A. supplies a range of computer hardware and software to 2000 schools within a large municipal region of Spain. When Coco S.A. won the contract the issue of customer service was considered to
In 12 consecutive innings a batman’s scores were: 6, 13, 16, 45, 93, 0, 62, 87, 136, 25, 14, and 31. Find his mean score and the median.
The distribution of insurance claims processed each day is presented in Table 2.3.Calculate the mean, mode, and median. Claims (X) Frequency (f) Table 2.3 1 3 2 4 3 4 LO 5 5 5 6 7 7 5 8 3 9 3 10 1
Bakers Ltd run a chain of bakery shops and is famous for the quality of its pies. The management of the company is concerned at the number of complaints from customers who say it takes too long to
The following are the IQs of 12 people: 115, 89, 94, 107, 98, 87, 99, 120, 100, 94, 100, 99. It is claimed that ‘the average person in the group has an IQ of over 100’. Is this a reasonable
Skodel Ltd is a small brewery that is undergoing a major expansion after a takeover by a large European brewery chain. Skodel Ltd produces a range of beers and lagers, and is renowned for the quality
Suppose that Karen’s statistics module is assessed via a series of assessments (multiple choice questions—mcq, in-course assignment—ica, end assignment—ea) with a weighting of 20%, 30%, and
Reconsider Example 2.1 and calculate measures of dispersion (or spread) of the statistics examination marks presented in Table 2.13.Data from Example 2.1Suppose the marks obtained in the statistics
A sample of six components was tested to destruction to establish how long they would last. The times to failure (in hours) during testing were 40, 44, 55, 55, 64, and 69. Which would be the most
Find the mean, median, and mode of the following set of data: 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5.
Cameos Ltd is employed by a leading market research organization based in Berlin. The company is discussing with the firm whether to expand the catering facilities provided to its employees to
The average salary paid to graduates in three companies is: £7000, £6000, and £9000 per annum respectively. If the respective number of graduates in these companies is 5, 12, and 3, fi nd the mean
Form a frequency distribution of the following data given in Table 2.10 with intervals centred at 10, 15, 20, 25, 30, 35, and 40, and estimate the mean value. 9 24 32 34 Table
The frequency distribution of the length of a sample of 98 nails is presented in Table 2.11 (measured to the nearest 0.1 mm).(a) Find the mean length of this sample by hand and by using a
The distribution of marks of 400 candidates in an A-level examination is presented in Table 2.12.(a) Calculate the mean value.(b) Construct the cumulative frequency curve and estimate the median, fi
Over a one-month period the number of vacant beds in a West Yorkshire hospital was surveyed. The frequency distribution in Table 2.17 resulted.Determine the mean and standard deviation. Beds
Greendelivery.com has recently decided to review the weekly mileage of the delivery vehicles used to deliver shopping purchased online to customer homes from a central parcel depot. The sample data
The manager at BIG JIMS restaurant is concerned about the time it takes to process credit card payments at the counter by counter staff . The manager has collected the following processing time data
The local regional development agency is conducting a major review of the economic development of a local community. One economic measure to be collected is the local house prices that reflect on the
CoCo S.A. are considering putting money into one of two investments, A and B. The net profits for identical periods and probabilities of success for investments A and B are given in Table 3.15.(a)
Over the last 3 years a random sample of 1000 students was selected and classified according to degree classification and gender. The results were as recorded in Table 3.2.Calculate: (a) The
Give an appropriate sample space for each of the following experiments:(a) A card is chosen at random from a pack of cards (b) A person is chosen at random from a group containing five females and
Bakers Ltd currently has 303 shops across the UK. Table 3.16 describes the location of each shop within one of four regions (SW, SE, NE, and ML and NW) and the level of shop profit.As part of Bakers
An experiment consists of throwing two dice and noting their two scores. The sample space could be shown as illustrated in Table 3.5.From this sample space calculate the following theoretical
For the respective sample spaces given in X3.1 indicate the outcomes that constitute the following events:(a) A queen is chosen(b) A female is chosen(c) A football team draws at least once.Data from
The Skodel Ltd credit manager knows from past experience that if the company accepts a ‘good risk’ applicant for a £60,000 loan the profit will be £15,000. If it accepts a ‘bad risk’
A card is chosen from an ordinary pack of cards. Write down the probabilities that the card is:(a) Black and an ace, (b) Black or an ace, (c) Neither black nor an ace. Let event A and B represent
A group of males and females over the age of 16 years; one is chosen at random. State which pair of events is mutually exclusive?(a) Being a male and being aged 21 years or older (b) Being a male
A dart is thrown at a board and is likely to land on any one of eight squares numbered 1–8 inclusive. A represents the event the dart lands in square 5 or 8. B represents the event the dart lands
How would you give an estimate of the probability of a 25-year-old passing a driving test at a first attempt?
Table 3.3 provides information about 200 school leavers and their destination after leaving school.Determine the probabilities that a person, selected at random:(a) Went into full-time education(b)
In an experiment we toss two unbiased coins 100 times and note the frequency of the two possible outcomes (heads, tails). We are interested in calculating the probability (or chance) that at least 1
An unbiased coin and a fair die are tossed together. What is the probability of obtaining a head and a 6?
Calculate the following probabilities if two unbiased dice are tossed: (a) The probability of a 3 on the first die and 5 on the second die = P(3, 5); (b) The probability of a 3 on the first die and
The following coins are placed in a bag: 1p, 2p, 5p, and 10p. A coin is taken at random and then replaced. A second coin is taken at random and then replaced. Calculate the following
Ten discs with a different number (0, 1, 2 . . .. 9) printed on them are placed in a bag.Two discs are taken out of the bag one at a time at random to form a two digit number (where 08 is counted as
A sample of 50 married women was asked how many children they had in their family. The results are presented in Table 3.6.Estimate the probability that if any married woman is asked the same
Five cards are labelled A1, B2, C3, D3, and E3 respectively. A card is selected at random and then a second is selected again before the first is replaced. (a) Show by listing the sample space that
For each question indicate whether the events are mutually exclusive: (a) Thermometers are inspected and rejected if any of the following are found: poor calibration; inability to withstand extreme
Consider two events, A and B, of an experiment which is not empty. Display this information in a Venn diagram and shade the area representing the event {A or B’}.
A survey shows that 80% of all households have a colour television and 30% have a microwave oven. If 20% have both a colour television and a microwave, what percentage has neither?
In a group of 50 students, 30 study French or German. If 20 study French and 15 study German fi nd the probability that a student studies French and German.
A bowl contains three red chips and five blue chips. Two chips are drawn successively, at random and without replacement. Calculate the probability that the first chip drawn is red and the second
Two events, D and E, are found to have the following probability relationships: P(D) = 1/3, P(E) = 1/4, and P(D or E) = 1/2. Calculate the following probabilities: (a) P(D and E), (b) P(D/E), (c)
Two events A and B are found to have the following probability relationships: P(A) = 1/3, P(B) = 1/2, and P(A or B) = 3/4. Calculate the following probabilities: (a) P(A/B), (b) P(B/A), (c)
A bag contains four red counters and six black counters. A counter is picked at random from the bag and not replaced. A second counter is then picked. Calculate the following probabilities: (a) The
The Gompertz Oil Company drills for oil in old oil fields that large companies have stated are uneconomic. The decision to drill will depend upon a number of factors, including the geology of the
A dart is thrown at a board and is equally likely to land in any one of eight squares numbered 1–8 inclusive. Let A = Event dart lands in square 5 or 8; B = Event dart lands in square 2, 3, or 4;
Each month DINGO Ltd receives a shipment of 100 parts from its supplier, which will be checked on delivery for defective parts. Historically, the average number of defective parts was 5. The new
Susan takes examinations in Mathematics, French, and History. The probability that she passes Mathematics is 0.7; the corresponding probabilities for French and History are 0.8 and 0.6. Given that
A manufacturing firm quality assures components manufactured and historically the length of a tube is found to be normally distributed with a population mean of 100 cm and a population standard
A bag contains six white and four red counters, three of which are drawn at random and without replacement. If X can take on the values of 0, 1, 2, 3 red counters, construct the probability
In a game you are offered the chance to toss a fair coin until a ‘tail’ appears. If a tail appears on the first toss you win £2. If the first tail appears on the second toss you win £4. If the
Use the NORM.DIST function to calculate the following probabilities, X ~ N(100, 25):(a) P(X ≤ 95); (b) P(95 ≤ X ≤ 105); (c) P(105 ≤ X ≤ 115); (d) P(93 ≤ X ≤ 99). For each
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
Bakers Ltd is currently in the process of reviewing the credit line available to supermarkets who they have defined as a ‘good’ or ‘bad’ risk. Based upon a £100,000 credit line the profi t
The manager at BIG JIMS restaurant is concerned about the time it takes to process credit card payments at the counter by counter staff .The manager has collected the following processing time data
Given that a normal variable has a mean of 10 and a variance of 25, calculate the probability that a member chosen at random is: (a) ≥ 11, (b) ≤ 11, (c) ≤ 5, (d) ≥ 5, (e) between 5 and
The lifetimes of certain types of car battery are normally distributed with a mean of 1248 days and standard deviation of 185 days. If the supplier guarantees them for 1080 days, what proportion of
A local authority surveyed the travel preferences of people who travelled to work by train or bus. The initial analysis suggested that one in five people travelled by train to work. If five people
Electrical resistors have a design resistance of 500 ohms. The resistors are produced by a machine with an output that is normally distributed N(501,9) ohms. Resistances below 498 ohms and above 508
A manufacturing company regularly conducts quality control checks at specifi ed periods on all products manufactured. A new order for 2000 light bulbs is due to be delivered to a national
A binomial model has n = 4 and p = 0.6.(a) Find the probabilities of each of the five possible outcomes (i.e. P(0), P(1) . . . P(4)).(b) Construct a histogram of this data.
A company is reviewing the number of telephone lines available for customer support. The average number of calls received per day is three calls during a five-minute period. Estimate the proportion
Attendance at a cinema has been analysed and shows that audiences consist of 60% men and 40% women for a particular film. If a random sample of six people was selected from the audience during a
In a large consignment of apples 3% are rotten. What is the probability that a carton of 60 apples will contain fewer than 2 rotten apples? We have here a binomial experiment and therefore could

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