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QBM117 Business Statistics

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Title: QBM117 Business Statistics


1
QBM117 Business Statistics
  • Introduction to Statistics

2
Objectives
  • To present a broad overview of statistics and its
    applications
  • To distinguish between a population and a sample
  • To distinguish between a parameter and a
    statistic
  • To distinguish between inferential statistics and
    descriptive statistics

3
Statistics
  • Statistics is the science of collecting,
    organising, presenting, analysing and
    interpreting data.
  • Statistics is often described as the science of
    decision making in the face of uncertainty.
  • Statistics is the scientific method that enables
    us to make effective decisions based on data.

4
Business Statistics
  • Statistics can be used in many fields of work and
    research.
  • Particularly in business, a major reason for
    collecting, organising, presenting, analysing and
    interpreting data is to give managers and
    decision makers a better understanding of the
    business environment.
  • This then allows them to make more informed and
    better decisions.

5
Applications of Business Statistics
  • Statistics may be applied in
  • Accounting
  • to select samples for auditing purposes
  • Economics
  • to analyse and predict the future of the economy
  • Finance
  • to track trends in financial measures over time

6
Applications of Business Statistics
  • Management
  • to manage and constantly improve production
    processes
  • Marketing
  • To conduct marketing research to decide whether
    and how they should market a product

7
Populations and Samples
  • In many situations, data are sought for a large
    group of items (individuals, stocks, voters,
    households, products, customers, and so on).
  • Because of time, cost and other restrictions,
    data are collected from only a small portion of
    the group.
  • The large group in a particular study is called
    the population, and then smaller group is called
    the sample.

8
Example 1
  • Suppose that a nationwide referendum is to be
    held in two weeks time where 10 million voters
    will indicate whether or not they are in favour
    of uranium mining. You are given the task of
    predicting what the outcome of the referendum
    might be.
  • To do this you could spend an enormous amount of
    time, money and effort to canvas the opinion of
    every eligible voter.

9
  • Instead, a sample of voters could be taken from
    the population of eligible voters, and the voting
    intentions of those in the sample recorded.
  • An estimate of the number of voters in the
    population who will vote for either choice could
    be based on the information from the sample.

10
Populations and Samples
  • A population is the entire collection of items
    about which information is desired.
  • A sample is a subset of the population that we
    collect data from.

11
Example 2 (Exercise 1.3 from text)
  • A politician who is running for the office of
    mayor of a city with 25 000 registered voters
    commissions a survey. In the survey, 48 of the
    200 registered voters interviewed say the planned
    to vote for her.
  • What is the population of interest?
  • The population of interest is the 25 000
    registered voters.

12
  • A politician who is running for the office of
    mayor of a city with 25 000 registered voters
    commissions a survey. In the survey, 48 of the
    200 registered voters interviewed say the planned
    to vote for her.
  • What is the sample?
  • The sample is the 200 registered voters who were
    interviewed.

13
Parameters
  • A parameter is a number that describes a
    population.
  • Examples are
  • - population mean, µ
  • - population standard deviation, s
  • - population proportion, p
  • A parameter is a fixed number.

14
Parameters
  • A statistic is a number that describes a sample.
  • Examples are
  • - sample mean,
  • - sample standard deviation, s
  • - sample proportion,
  • A statistic is a variable whose value varies from
    sample to sample.

15
Example 2 revisited
  • A politician who is running for the office of
    mayor of a city with 25 000 registered voters
    commissions a survey. In the survey, 48 of the
    200 registered voters interviewed say the planned
    to vote for her.
  • Is the value 48 a parameter or a statistic?
  • It is a statistic as it is a descriptive measure
    obtained from the sample.

16
Descriptive and Inferential Statistics
  • Statistics can be subdivided into two basic
    areas
  • Descriptive Statistics
  • Inferential Statistics

17
Descriptive Statistics
  • Most of the statistical information in
    newspapers, magazines, reports, and other
    publications consists of data that are summarized
    and presented in a form that is easy for the
    reader to understand.
  • Such summaries of data are referred to as
    descriptive statistics.

18
Descriptive Statistics
  • Descriptive Statistics involves collecting,
    organising, summarising and presenting numerical
    data.
  • This includes
  • - graphical displays
  • - condensation of data into tables
  • - calculation of summary measures

19
Inferential Statistics
  • Because populations are very large, it is
    impractical and expensive to investigate or
    survey every member of a population.
  • It is far easier and cheaper to take a sample
    from the population of interest and to draw
    conclusions about the population based on the
    information provided by the sample.
  • Inferential Statistics involves drawing
    conclusions about a population based on the
    sample information.

20
Inferential Statistics
  • In practice we usually dont know the value of a
    population parameter.
  • We take a sample from the population of interest
    and calculate the sample statistic.
  • We then use the sample statistic to estimate the
    parameter of interest.
  • This is known as statistical inference.

21
Example 3
  • A survey of starting salaries for 2000 tertiary
    graduates with degrees in economics was conducted
    in April 2001. The survey reported on average
    annual starting salary of 30 000. This survey
    result was based on a nationwide sample of 400
    tertiary graduates who had accepted job offers
    during December 2000.
  • What is the population of interest?
  • The population of interest is 2000 tertiary
    graduates with degrees in economics.

22
  • A survey of starting salaries for 2000 tertiary
    graduates with degrees in economics was conducted
    in April 2001. The survey reported on average
    annual starting salary of 30 000. This survey
    result was based on a nationwide sample of 400
    tertiary graduates who had accepted job offers
    during December 2000.
  • What is the sample?
  • The sample is the 400 tertiary graduates
    surveyed.

23
  • A survey of starting salaries for 2000 tertiary
    graduates with degrees in economics was conducted
    in April 2001. The survey reported on average
    annual starting salary of 30 000. This survey
    result was based on a nationwide sample of 400
    tertiary graduates who had accepted job offers
    during December 2000.
  • Is the average annual salary of 30 000 a
    parameter or a statistic?
  • It is a statistic as it is the average annual
    starting salary of the sample.

24
Example 4
  • A telemarketing firm in Sydney uses a device
    that dials residential telephone numbers in that
    city at random. Of the first 100 numbers dialled,
    43 are unlisted. This is not surprising, because
    52 of all Sydney residential phones are
    unlisted.
  • What is the population?
  • The population is all Sydney residential phones.

25
  • A telemarketing firm in Sydney uses a device
    that dials residential telephone numbers in that
    city at random. Of the first 100 numbers dialled,
    43 are unlisted. This is not surprising, because
    52 of all Sydney residential phones are
    unlisted.
  • What is the sample?
  • The sample is the first 100 numbers dialled.

26
  • A telemarketing firm in Sydney uses a device
    that dials residential telephone numbers in that
    city at random. Of the first 100 numbers dialled,
    43 are unlisted. This is not surprising, because
    52 of all Sydney residential phones are
    unlisted.
  • What is the parameter?
  • The parameter is the proportion of Sydney
    residential phones that are unlisted, i.e. 52.

27
  • A telemarketing firm in Sydney uses a device
    that dials residential telephone numbers in that
    city at random. Of the first 100 numbers dialled,
    43 are unlisted. This is not surprising, because
    52 of all Sydney residential phones are
    unlisted.
  • What is the statistic?
  • The statistic is the proportion of Sydney
    residential phones in the sample that are
    unlisted, i.e. 43 (43 out of 100).

28
Example 5
  • A golf ball manufacturer wishes to know how far
    its newly designed super fly golf ball will go.
  • What is the population of interest?
  • The population of interest is all super fly golf
    balls produced by the manufacturer.

29
  • A golf ball manufacturer wishes to know how far
    its newly designed super fly golf ball will go.
  • Suggest possible reasons for taking a sample?
  • It would take too much time and money to test
    each super fly gold ball.
  • And it is unlikely that a super fly golf ball
    can be sold after it has been tested. So, if
    every golf ball was tested, there would be no
    golf balls to sell.

30
  • A golf ball manufacturer wishes to know how far
    its newly designed super fly golf ball will go.
  • What is the parameter of interest?
  • The parameter of interest is the average
    distance a super fly golf ball travels after it
    is hit.

31
  • A golf ball manufacturer wishes to know how far
    its newly designed super fly golf ball will go.
  • What statistic might you calculate from the
    sample?
  • The statistic to calculate is the average
    distance travelled by the super fly golf balls in
    the sample.

32
Example 6 (Exercise 1.4 from text)
  • A manufacturer of computer chips claims that
    less than 10 of his products are defective. When
    1000 chips were drawn from a large production
    run, 7.5 were found to be defective.
  • What is the population of interest?
  • The population of interest is all of the
    computer chips produced by the manufacturer.

33
  • A manufacturer of computer chips claims that
    less than 10 of his products are defective. When
    1000 chips were drawn from a large production
    run, 7.5 were found to be defective.
  • What is the sample?
  • The sample is the 1000 chips drawn from the
    large production run.

34
  • A manufacturer of computer chips claims that
    less than 10 of his products are defective. When
    1000 chips were drawn from a large production
    run, 7.5 were found to be defective.
  • What is the parameter?
  • The parameter is the proportion of defective
    chips in the population,
  • i.e. the proportion of defective chips produced
    by the manufacturer.

35
  • A manufacturer of computer chips claims that
    less than 10 of his products are defective. When
    1000 chips were drawn from a large production
    run, 7.5 were found to be defective.
  • What is the statistic?
  • The statistic is the proportion of defective
    chips in the sample, i.e. 7.5.

36
  • A manufacturer of computer chips claims that
    less than 10 of his products are defective. When
    1000 chips were drawn from a large production
    run, 7.5 were found to be defective.
  • Does the value 10 refer to the parameter or the
    statistic?
  • The value 10 refers to the parameter.

37
  • A manufacturer of computer chips claims that
    less than 10 of his products are defective. When
    1000 chips were drawn from a large production
    run, 7.5 were found to be defective.
  • Is the value 7.5 a parameter or a statistic?
  • The value 7.5 is a statistic as it is the
    proportion of defective chips in the sample.

38
  • A manufacturer of computer chips claims that
    less than 10 of his products are defective. When
    1000 chips were drawn from a large production
    run, 7.5 were found to be defective.
  • Explain briefly how the statistic can be used to
    make inferences about the parameter to test the
    claim.
  • The sample proportion of defective chips (7.5)
    is less than 10 and hence there is evidence to
    support the manufacturers claim.

39
Check your understanding
  • What is the difference between a sample and a
    population?
  • What is the difference between a statistic and a
    parameter?
  • What is the difference between descriptive and
    inferential statistics?

40
Reading for next lecture
  • SS Chapter 2, Sections 2.1-2.3
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