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Flow Diagram for The inference about two populations and ANOVA

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Title: Flow Diagram for The inference about two populations and ANOVA


1
Flow Diagram for The inference about two
populations and ANOVA
  • To help identify the procedure to use in
    performing inference type analysis we need to ask
    a few questions, and pay attention to the
    answers.
  • The next slide provides a flow diagram that helps
    you determine the proper procedure to apply.

2
The Flow Diagram
2 Populations
3 Populations
3
Review Problem 1
  • One factor in low productivity is the amount of
    time wasted by workers. Wasted time includes time
    spent cleaning up mistakes, waiting for more
    material and equipment, and performing any other
    activity not related to production. In a project
    designed to examine the problem, an operations
    management consultant took a survey of 200
    workers in companies that were classified as
    successful (on the basis of their latest annual
    profits) and another 200 workers from
    unsuccessful companies. The amount of time (in
    hours) wasted during a standard 40-hour workweek
    was recorded for each worker. These data are
    stored in columns 1 (successful companies) and 2
    (unsuccessful companies) in file Productivity.

4
  • Do these data provide enough evidence at the 1
    significance level to infer that the amount of
    time wasted in unsuccessful firms exceeds that of
    successful ones?
  • Estimate with 95 confidence how much more time
    is wasted in unsuccessful firms than in
    successful ones.productivity.xls

5
Review problem 2
  • Ikarus, the Hungarian bus maker, has lost its
    important CIS market and is reported on the verge
    of collapse. The company is now trying a new
    engine in its buses and has gathered the random
    samples of miles-per-gallon figures for the old
    engine versus the new provided in file Ikarus.
  • Is there evidence that the new engine is more
    economical than the old one?Ikarus.xls

6
Review Problem 3
  • The president of a large company is in the
    process of deciding whether to adopt a lunchtime
    exercise program. The purpose of such programs is
    to improve the health of workers and, in so
    doing, reduce medical expenses. To get more
    information she instituted an exercise program
    for the employees in one office. The president
    knows that during the winter months medical
    expenses are relatively high because of the
    incidence of colds and flu. Consequently, she
    decides to record medical expenses for the 12
    months before the program and for 12 months after
    the program. The "before" and "after" expenses
    (in thousands of dollars) are compared on a
    month-to-month basis and shown in file Expenses.

7
  • Do the data indicate that exercise programs
    reduce medical expenses? (Test with a .05.)
  • Estimate with 95 confidence the mean savings
    produced by exercise programs.Expenses.xls

8
Review Problem 4
uh ah.xls
  • A study performed by a Columbia University
    professor (described in Report on Business,
    August 1991) counted the number of times per
    minute professors from three different
    departments said "uh" or "ah" during lectures to
    fill gaps between words. The data derived from
    observing 100 minutes from each of the three
    departments are stored in file uh-ah (Column 1
    contains all the data for the English department,
    column 2 stores the data for the mathematics
    department, and column 3 stores the data for the
    political science department.) If we assume that
    the more frequent use of "uh and "ah" results in
    more boring lectures, can we conclude at the 5
    significance level that some departments'
    professors are more boring than others?

9
Review Problem 5
  • The friendly folks at the IRS are always looking
    for ways to improve the wording and format of its
    tax return forms. Three new forms have been
    developed recently. To determine which, if any,
    are superior to the current form, 120 individuals
    were asked to participate in an experiment. Each
    one of the three new forms, as well as the
    currently used form, were filled out by 30
    different people. The amount of time (in
    minutes) taken by each person to complete the
    task was recorded and stored in File IRS. The
    sample means and standard deviations were
    computed as follows.

10
  • Form 1 mean 90.17, standard deviation 31.49.
  • Form 2 mean 95.77, standard deviation 30.01.
  • Form 3 mean 106.83, standard deviation
    30.47.
  • Form 4 mean 111.17, standard deviation 31.99
  • What conclusion can be drawn from these data?
    (Use ? .05)
  • What are the required conditions for the test
    conducted above? Does it appear that the
    required conditions of the test are satisfied?
    IRS.xls
  • Can you determine which one of the forms takes
    the shortest time to fill in? Use a .05

11
Review Problem 6
  • Many North Americans suffer from high levels of
    cholesterol, which can lead to heart attacks. For
    those with very high levels (over 280), doctors
    prescribe drugs to reduce cholesterol levels. A
    pharmaceutical company has recently developed
    three such drugs. To determine if any differences
    exist in their benefits, an experiment was
    organized. The company selected 25 groups of
    three men, each of whom had levels in excess of
    280. In each group, the men were matched
    according to age and weight. The drugs were
    administered over a two-month period, and the
    reduction in cholesterol was recorded. The data
    are stored in the first three columns of file
    Cholesterol. Do these results allow the company
    to conclude at the 5 significance level that
    differences exist among the three new drugs?

12
Review Problem 7
  • Phonex provides call center services for many
    different companies. One of four cities is being
    considered where a new call center is to be
    established. Managers will have to be transferred
    to the new location, and Phonex tries to find
    whether differences in housing prices exist
    across the competing cites. Having concerns about
    the large variability among house prices due to
    house age and size, each house observed was
    classified by age category and size category, and
    its price then recorded. See Phonex.xls.
  •  
  • a. At 5 significance level, is there a
    difference in the average house price between
    Wichita and Little-Rock?
  • b.    At 5 significance level, is there
    evidence to conclude that the average price of
    houses of the category predefined is not the
    same in the four cities? What assumption do you
    need to make to run your test?

13
Review Problem 8
  • GroBros., A regional grocery store chain, is
    considering to upgrading to a new series of price
    scanners. Scanners sometimes have errors, and
    GroBros. wants to evaluate the average levels of
    such errors for 4 different types of scanners(the
    current one, and three new ones). Thirty
    different shopping baskets were defined (which
    differ in the number of items, and the types of
    items included). Each basket was scanned four
    times (by each scanner) and then item prices were
    determined by hand. The number of scanning errors
    in each basket was recorded. See file
    GroBros.xls.
  •  
  • a.   State the hypothesis of interest for this
    test.
  • b.  At 1 significance level, is there a
    difference between the number of errors among
    the scanners?
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