Hypothesis Testing

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Hypothesis Testing

• (Lesson - 04/B)
• Is it or is it not?

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Chapter Outcomes

• After studying the material in this chapter, you
  should be able to
• Formulate null and alternative hypotheses for
  applications involving a single population
  mean, variance, or proportion.
• Correctly formulate a decision rule for testing
  a null hypothesis.
• Know how to use the p-value, test statistic, and
  critical value, approach to test the null
  hypothesis.

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Hypothesis Testing

• The hypothesis testing is testing a plausible
  answer (proposition hypothesis) to a question by
  expressing it in two contradicting propositions
  (hypothesis) The null hypothesis (H0) and the
  alternative hypothesis (HA).
• How long does it take to process a guest at the
  front desk?
• H0 Processing a guest at the front desk takes 3
  minutes or less.
• HA Processing a guest at the front desk does not
  take 3 minutes or less.

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Formulating the Hypothesis

• The null hypothesis is a statement about the
  population value that will be tested.
• H0 Processing a guest at the front desk takes 3
  minutes or less.
• The null hypothesis will be rejected only if the
  sample data provide substantial contradictory
  evidence.

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Formulating the Hypothesis

• The alternative hypothesis is the hypothesis that
  includes all population values not covered by the
  null hypothesis.
• HA Processing a guest at the front desk does not
  take 3 minutes or less.
• The alternative hypothesis is deemed to be true
  if the null hypothesis is rejected.

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Hypothesis Set-up

• Ready to use statistical tests have their Ho
  already set up.
• For example
• for Normality test Ho series are normally
  distributed
• for Correlation test Ho there is no
  relationship between the series.
• In case of tests for special problems we need to
  set up the Null Hypothesis using some general
  rules.

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Hypothesis Set-up

• To set-up a Null Hypothesis there are three rules
  with the following order
• Burden of Prove should be with the claim, (so,
  claims should be expressed as Ha, since Ho
  is harder to reject)
• In general what is important should be expressed
  as Ha (Statement of Claim, Investigation,
  Expectation, etc.)
• Use Common Sense,
• Have a positive approach.

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Hypothesis Set-up (cont.)

• Example-1
• New has the burden of prove since it has
  inherent claim that it is more efficient or
  effective than the old.
• new process - old process
• new drug - old drug
• new machine - old machine

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Hypothesis Set-up (cont.)

• Exampl-2
• Management/Company has burden of proof since it
  has power to make false claims
• Claim on the performance of an employee
• (employee protection)
• Claim on the performance of a product
• (consumer protection)

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Hypothesis Set-up (cont.)

• Exampl-3
• Government has burden of proof since it has
  power to make false claims
• Claim on violation of a low

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Types of Statistical Errors

• Type I Error - This type of statistical error
  occurs when the null hypothesis is true and is
  rejected.
• Type II Error - This type of statistical error
  occurs when the null hypothesis is false and is
  not rejected.

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Types of Statistical Errors
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Establishing the Decision Rule

• The job of the decision maker is to establish a
  cutoff point, called a critical value.
• The cutoff point is the demarcation between
  failing to reject and rejecting the null
  hypothesis.
• When critical value is stated in terms of the
  hypothesized mean it is labeled ?0.

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Establishing the Decision Rule

• The critical value is the value of a statistic
  corresponding to a given significance level.
  This cutoff value determines the boundary between
  the samples resulting in a test statistic that
  leads to rejecting the null hypothesis and those
  that lead to a decision not to reject the null
  hypothesis.

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Establishing the Decision Rule

• The significance level is the maximum probability
  of committing a Type I statistical error. The
  probability is denoted by the symbol ?.

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Next Lesson

• (Lesson - 04/C)
• Statistical Decision and
• 1-Sample Hypothesis Testing