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7.1 Introduction to Hypothesis Testing

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7.1 Introduction to Hypothesis Testing Key Concepts: Hypothesis Tests Type I and Type II Errors Probability Value (or P-value) of a Test Decision Rules – PowerPoint PPT presentation

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Title: 7.1 Introduction to Hypothesis Testing


1
7.1 Introduction to Hypothesis Testing
  • Key Concepts
  • Hypothesis Tests
  • Type I and Type II Errors
  • Probability Value (or P-value) of a Test
  • Decision Rules

2
7.1 Introduction to Hypothesis Testing
  • Consider the following scenario
  • A fluorescent lamp manufacturer guarantees that
    the mean life of a certain type of lamp is at
    least 10,000 hours. You want to test this
    guarantee. To do so, you record the life of a
    random sample of 32 fluorescent lamps (see
    below). At a 0.09, do you have enough evidence
    to reject the manufacturers claim? (42 p. 376)
  • 8,800 9,155 13,001 10,250 10,002 11,413 8,234 10,
    402
  • 10,016 8,015 6,110 11,005
    11,555 9,254 6,991 12,006
  • 10,420 8,302 8,151 10,980 10,186
    10,003 8,814 11,445
  • 6,277 8,632 7,265 10,584 9,397
    11,987 7,556 10,380

3
7.1 Introduction to Hypothesis Testing
  • How can we test such claims?
  • Start with a pair of statistical hypotheses or
    statements about a population parameter.
  • Null Hypothesis Ho
  • Statistical hypothesis that contains a statement
    of equality like , , or .
  • Alternative Hypothesis Ha
  • The complement of the null hypothesis. It is a
    statement that must be true of the null
    hypothesis if false.
  • Practice forming Ho and Ha.
  • 12 p. 359
  • 16

4
7.1 Introduction to Hypothesis Testing
  • When we conduct hypothesis tests, we always work
    under the assumption that the null hypothesis is
    true. We will reject Ho only when there is
    enough evidence to do so.
  • We need to be aware of two types of errors that
    may occur in a study
  • A type I error occurs if a true null hypothesis
    is rejected.
  • A type II error occurs if a false null hypothesis
    is not rejected.
  • Practice Identifying Errors
  • 32 p. 360 (Flow Rate)

5
7.1 Introduction to Hypothesis Testing
  • Definitions and Symbols we will need later
  • The probability of making a type I error is known
    as the significance level of the test and is
    denoted by a.
  • The probability of making a type II error is
    denoted by ß.

6
7.1 Introduction to Hypothesis Testing
  • Once we have identified Ho, Ha, and a, we need to
    calculate the value of a test statistic and then
    use it to make a decision about Ho.
  • Once way to make that decision is to use the
    probability value or P-value of the test.
  • P-value the probability of obtaining a sample
    statistic with a value as extreme as or more
    extreme than the one determined from the sample
    data.
  • The way we calculate the P-vale of a test depends
    on the type of test we are working with
    (left-tailed, right-tailed, or two-tailed). See
    page 354.
  • Practice identifying the type of test
  • 38 p. 360 (Clocks)
  • 40 p. 360 (Lung Cancer)

7
7.1 Introduction to Hypothesis Testing
  • How do we decide whether or not to reject the
    null hypothesis?
  • We use decision rules based on the P-value
  • If the P-value of the test is less than or equal
    to the significance level, we reject Ho.
  • If the P-value of the test is greater than the
    significance level, we do not reject Ho.
  • Note If we do not reject the null hypothesis,
    it doesnt mean we are saying Ho is true. We are
    saying we do not have enough evidence to reject
    Ho.
  • 46 p. 361 (Gas Mileage)
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