Chapter 7 Inference for Distributions

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Chapter 7Inference for Distributions

• 7.1 Inference for the Mean of a Population
• 7.2 Comparing Two Means
• 7.3 Inference for Population Spread

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Section 7.1 Inference for the Mean of a
Population ?????????
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???????

• ????????????(SRS),???? n
• ????????,???? m ????s??????,m ?s ????
• ???,???????,????????????

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???????

• ????????????,??????? ???? N(m, s2/n )
• ???s ??,?????? s ???
• ? ??????????
• ? ??????? t ??

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????(standard error)

• ??????? ??? ????? (standard error
  of mean, ???SEM)
• When the standard deviation of a statistic is
  estimated from the data, the result is called the
  standard error of the statistic.

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t ???? t ??

• ???? N(m, s2),??????,???? n
• ????? t ??? (one-sample t statistic)?
• ? t ????????? n-1? t ??
• ? t(k)? tk ?????? k ? t ??
• t ?????????????? s ????

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????? t ????
??????
t ?????9
t ?????2
0
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??? t ????????

• t ?????????????
• ????????????????
• t ???????(spread)????????, t ??????????????
• ? ?? ????,?? t ??????????
• t ????????????????
• ????? s ?? s ??,??????????????

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?????? t ????

• ????? m ???,????????,???? n?m ?C???????
  ??t? tn-1????(1-C)/2????
• ?????????????(exact)??,??????????????(approximate)
  ???

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?????? t ??

• ????? m ???,????????,???? n? H0m m0
  ??????????
• ?T ?? tn-1?????????P-??
• Ham gt m0 ? P-?? ?
• Ham lt m0 ? P-?? ?
• Ham m0 ? P-??
• ???????????????,????????????????

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??7.1 ????????

• 5????????10???,????????(??)
• 55.95 68.24 52.73 21.50 23.78
• 44.44, s 20.741
• 95????? tn-1???? t 2.776
• 95????? (18.69, 70.19)

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??7.2 ????

• ?6.8?10??????????????????
• 2.0 0.4 0.7 2.0 -0.4 2.2 -1.3 1.2 1.1
  2.3
• ?? H0m 0 vs. Ham gt 0
• 1.02, s 1.196
• t?? P-?
  0.0122?
• df 9 ? P-??

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t ?? P-?????
t ?????9
P-? 0.0122
t 2.70
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???? t ?????????

• ???,????????????SRS??
• ??????,???????????,??????????????????????
• Fortunately, confidence levels and P-values from
  t procedures are not very sensitive to lack of
  normality.
• ? 7.1 ? 7.2 ???????

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• Stem-and-leaf of t71 N 5
• Leaf Unit 1.0
• 2 2 24
• 2 3
• 2 4
• (2) 5 36
• 1 6 8

• Stem-and-leaf of t72 N 10
• Leaf Unit 0.10
• 1 -1 3
• 2 -0 4
• 4 0 47
• (2) 1 12
• 4 2 0023

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????? t ??

• ??????(matched pairs design)
• ?????????????????
• Or ????????????????
• ????? t ??
• ????? t ??????????????

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??7.3 ?????????

• ???????????????????????
• 21?????????????????,????????????,?????????????????
  ?????
• ?? m ????(????)???????????????????,?
• ???? H0m 0 vs. Ham gt 0

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?????????(?)

• ???????? s 12.5479
• ?? t-????
• P-???0.25 (?C, df 20)
  ?????P-??0.3652 ?

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t ??????(Robustness)

• ????(robust procedures)??????????????
  P-?,????????????????,???????????
• ???????????,?????????? t ??????,?? t ?????????????

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??7.4 ?????

• ??7.1?????
• 55.95 68.24 52.73 41.50 43.78 (???20)
• ? ? 44.44??52.44,
• s? 20.741??10.69
• 95????? tn-1????? t 2.776
• 95????????? 52.44?14.8377
  (37.60, 67.28)

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t ???????

• ???????,???????????????
• ?????15?,?????????????????? t ??
• ?????15?,??????????????????,???? t ??
• ?????(n ? 40)?,??????????? t ??

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t ???????

• Figure 7.6a ????65????????????,????,??????t ???

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t ???????(?)

• Figure 7.6b ??????????????????,????70,????t ???

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t ???????(??)

• Figure 7.6c ???????????????????,?????????????????
  ,???t ???