STAT 235 LABRATORY

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STAT 235 LABRATORY

• Laboratory 3
• --- Confidence Intervals and
• Hypothesis Testing

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Confidence Intervals

• Purpose to estimate an unknown population
  parameter with and indication of how accurate the
  estimate is.
• Two parts of confidence intervals an interval
  computed form the sample and a confidence level
  (Usually, denoted by C).
• Examples
• Population mean
• Population standard deviation

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Confidence Intervals ---Contd

• Normal population with known S.D. s2
• where z is the upper value of N(0,1), say,
  z 1.96 if C95. N is the sample size.
• Normal population with unknown S. D.
• where t is the upper value of tn-1 and n is
  the sample size.

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Confidence Intervals ---Contd

• Margin of error half of the interval range
• Both z and t increase as the confidence level
  C increases. So does the margin of errors.
• The margin of error decreases as the sample size
  increase for fixed population S.D. (s).
• Use descriptive statistic to obtain 95 C.I. for
  normal population mean with unknown S.D..

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Hypothesis Testing

• Five steps to perform a hypothesis test
• Hypothesis
• Test Statistic and its distribution
• Value of test statistics, denoted by T.
• P-value
• Conclusions
• Two type errors
• Type I Reject H0 when it is true
• Type II Not reject H0 when it is false

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Hypothesis Testing---Contd

• Two tailed and one tailed tests
• Test statistic for two sample t-test assuming
  unequal variance
• What is n?

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Hypothesis Testing---Contd

• Two sample t-test in Excel
• Tools ? data analysis ? t-test two sample
  assuming unequal variance
• Specify data, hypothesis, and alpha.
• We can obtain
• Value of test statistics---t Stat
• n---Df
• P-value---P(Tltt)one-tail or P(Tltt)two-tail
• Confidence level and significance level

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Questions

• Do You Have Any Questions?
• Follow the Lab Instructions, Try Yourself.
• Due Date Friday, Mar, 23 by 1000 PM
• Good Luck and Have Fun!