Statistical Analysis 2

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- Statistical Analysis 2 -
Topic 9
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T-test Z-test

• Deal with only one metric question
• Test the hypothesis about the mean
• Whether to use T-test or Z-test?
• Depend on the sample size
• If n30, use Z-test
• If n
• Determine whether the test is one-tailed or
  two-tailed

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Formula for T-test Z-test
Z-test T-test

• where
• Xbar mean of the sample
• µ mean of the population (value in H0)
• standard error of the mean

d.f. n-1
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Example 1 (T-test Z-test)

• EPA (Environmental Protection Agency) evaluated
  the mileage claims of Ford automobiles by
  obtaining a random sample of 100 Ford cars to
  make sure that the mileage is greater than 30
  miles per gallon (mpg). If mileage is greater
  than 30 mpg, EPA has the authority to give tax
  exemptions to Ford. The sample mean mpg achieved
  was 33.6, and the standard error was 1.2 mpg.
  What should EPA do? (give tax exemptions or not)

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Example 2 (T-test Z-test)

• In a test marketing study, the average sales for
  a new brand of shampoo in 10 stores is 2020
  bottles, standard error is 20. The retail
  management is expecting to sell at least an
  average of 2000 units for the product to be
  considered successful and therefore launch it at
  national level. Is the product successful
  according to managements expectation?

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Example 3 (T-test Z-test)

• A manufacturer of automobile windshield has to
  produce windshields that can obtain a quality
  rating of 5,000 points. Based on past experience,
  the manufacturer knows that the standard error of
  quality rating is 25. To check the quality, the
  management picks a random sample of 100
  windshields and finds that the mean quality
  rating is 4,960. Based on this sample, the
  management wants to know whether its products
  meets the quality standard and is neither higher
  nor lower.

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ANOVA

• ANalysis Of VAriance (ANOVA)
• Deal with only two questions
• One non-metric
• One metric
• Test of means for two or more groups
• One-tailed test

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ANOVA

• Null hypothesis (H0) no difference between means
  of all groups
• Alternative hypothesis (H1) at least there is
  one mean different from others

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Example 1 (ANOVA)

• Suppose your household were to select a telephone
  calling card. Please rate the importance of easy
  to use this attribute. (5 is denoted as very
  important, and 1 is denoted as very
  unimportant.)
• From the data, can we say that there is no
  difference on the importance of easy to use
  between groups?

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Example 2 (ANOVA)

• Please indicate your opinion as to the extent to
  which you agree or disagree with the statement
  The prices are reasonable for Publix. (7 is
  denoted as strongly agree, and 1 is denoted as
  strongly disagree.)
• From the data, can we say that there is no
  difference on the agreement between groups for
  this statement?