Statistics%20201%20

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Statistics 201 Lecture 24
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Back to Significance Testing

• Four Basic Steps
• State hypothesis (in terms of pop. parameter)
• Calculate test statistics
• Find p-value (WILL NOT DO RECTION REGION)
• State Conclusion in terms of real problem at hand

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Z-Test for a Population Mean (Known Standard
Deviation)

• Data random sample x1, x2, , xn from a N(m, s)
  population
• Mean, m, is unknown
• Standard deviation, s, is known
• For testing the hypothesis H0 mm0
• Test Statistic

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Z-Test for a Population Mean (Known Standard
Deviation)

• Computing p_value depends on the alternate
  hypothesis

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Example

• A student group claims that first year students
  at a university study 2.5 hours per weeknight
• A skeptical statistics professor claims that this
  is waaaay too high
• A random sample of 269 university students found
  an average study time of the students to be 137
  minutes
• Suppose that the study times follow a normal
  distribution with standard deviation of 65
  minutes
• Using these data test the profs hypothesis with
  a sig. level of 0.01

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Example

• Hypotheses
• Test Statistic
• P-value
• Conclusion

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Example

• IQ test scores of 7th grade girls in the Midwest
  USA follow a normal distribution with standard
  deviation of 15
• A random sample of 31 7th grade girls from a
  Midwest school district is taken and their IQs
  measuredgiving a sample mean of 104
• IQs in the broad population supposed to have an
  average of 100
• Is there evidence at a 0.05 level that the mean
  in this district is different from the mean in
  the general population?

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Example

• Hypotheses
• Test Statistic
• P-value
• Conclusion