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					             Stat 217 – Lecture 12

The National Transportation Safety Board recently divulged a highly secret plan
they had funded with the U.S. auto makers for the past five-years. The NTSB
covertly funded a project whereby the auto makers were installing black boxes
in four wheel drive pick-up trucks in an effort to determine, in fatal accidents,
the circumstances in the last 15 seconds before the crash.

They were surprised to find in 49 of the 50 states the last words of drivers
in 61.2% of fatal crashes were, "Oh, Shit!"

Only the state of Texas was different, where 89.3% of the final words were,
"Hey Y'all, watch this!"
• Exam Wednesday
  – Go to opposite room than you went to last
  – Halfway through will be able to switch rooms
• Review session
  – Tuesday 7:30-9, Building 53-Room 213
• Next Monday
  – Third project report – where are you at?
  Last Time – Confidence Intervals

• Especially if we reject a hypothesized value for
  the parameter, can follow up by determining
  what are plausible values for the parameter.
  Proportion p               Mean m

 Technical Conditions      Technical Conditions
• SRS                      SRS
• n ,n(1- ) > 10           n>30 or pop Normal
                Lab 4
• What do we mean by “confidence”

              If construct many, many intervals
              from many, many random samples, in
              the long run, 95% of the intervals
              succeed in capturing the parameter
       Example 11-3 (p. 102)
• (d) A 99% confidence interval is wider
  than a 90% confidence interval
• (f)
Example 11-4, 11-5
Example 11-6
            Sleeping Times
• Example 10-3 (p. 92) , part (a)
Is there evidence that Cal Poly students
  average less than seven hours of sleep?
Is there evidence that Cal Poly students
  average less than eight hours of sleep?
• Example 12-3 (p. 114)
90% confidence interval for m?
Example 10-3 cont.
            Sleeping Times
• If all else the same, but standard deviation
  is larger, will have a larger p-value.
        Reducing Variability
• Much easier to see a difference if there is
  less variability
  – increase sample size
  – decrease variability in data
                   Lab 3
• Key idea: reduce variability

• Why do these prices vary?
                    Lab 3
• By “pairing” the items, have explained
  some of the variation.
• This reduction in variability makes it easier
  to see differences between the 2 stores
  – The only difference between the items in the
    pair should be the store = explanatory variable
                   Lab 3
• Removing items
• Sampling distribution of means
  – What does the Central Limit Theorem tells us?
  – What does this mean?

• See sample on web
            Common Mistakes
• bias vs. precision
   – representative: is sample random
   – accurate/precision: how close together
   – reliable: does method work
• z vs. t
   – use z with proportions (Table A)
   – use t with means (Table C or IV)
• stating hypotheses about statistic/nothing
   – H0: = .5
          Types of Problems
• Probability calculations for a sampling
  – if p=.2, what is the probability <.1
• Test of significance
  – is there statistically significant evidence that…
• Confidence intervals
  – estimate value of population parameter
• Interpretation
  – including “what if”
     Test of Significance Steps
•   Define parameter in words
•   State hypotheses about parameter
•   Check technical conditions and sketch
    sampling distribution if met
•   Calculate test statistic
•   Calculate p-value (state df with t)
•   Make conclusion: reject or fail to reject Ho
•   Answer the research question
      Confidence Interval Steps
•   Define parameter
•   Check technical conditions
•   Calculate confidence interval
•   Provide summary statement
    – I’m 95% confident that…

• Be able to interpret confidence without
  using “confidence” “sure” “certain”…
• What does “confidence” mean?
  – What affects width?
• What does “p-value” mean?
  – What affects value?
• What is it a probability of?
  – what is “random”?
  – what is it a distribution of?
  – Draw and label a picture!
• Work problems
  – PLEASE review solutions on web
     – hw, labs, examples, old quiz solutions, etc.
  – start with a picture (maybe not with ci)
• See if you can identify which type of
  problem you have
• Think about what each step means
• Banish the word IT
• Add the phrase “of what” and “for what”

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