Stat 100 Mar. 18

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Stat 100 Mar. 18
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Stat 100

• Read Ch. 18, Try 1-6,10-11
• Read Ch. 19, Try 1-7

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Commonplace objective

• Use a sample to estimate something about a
  population
• For instance, what percent of the PSU population
  thinks there should be 14-week semesters?
• Or, what is mean hours of study per week for PSU
  students?

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Recent Gallup Poll

• 34 of n1,012 said there was an area within a
  mile of home where theyd be afraid to walk alone
  at night
• This is a sample estimate of a population value
• Reported margin of error 3

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Margin of Error

• Likely upper bound on sampling error
• For 95 of random samples of a specific size,
  sampling error is less than the margin of error.

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Confidence Interval

• An interval of values that is likely to include
  the true population value.
• Compute Sample value margin of error
• For walk alone at night question, confidence
  interval is 34 3
• This interval is likely to include percent afraid
  to walk alone for whole population

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Confidence Level

• Probability that confidence interval catches the
  population value
• Confidence is actually in the procedure.
• To be 95 confident means that 95 of the time,
  the procedure provides an interval that catches
  the population value

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95 confidence most common

• Most polls (including Gallup) report margin of
  error for 95 confidence

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Another Crime Poll Results

• 22 said crime was an extremely serious problem
  in the U.S.
• A 95 confidence interval for the population
  percent who thinks this is 223

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Conservative Calculation

• 95 margin of error
• Provides value larger than actual error in at
  least 95 of all samples.

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Examples of Margin of Error

• n400, 1/sqrt(400) 0.05 or 5
• n1000, 1/sqrt(1000)0.03, or 3
• n2500, 1/sqrt(2500)0.02, or 2
• Notice that big increase in sample size needed to
  drop m.e. from 3 to 2

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More Exact Margin of Error

• 95 m.e. 2

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For Serious Crime Question

• p0.22 , n1012
• Sqrt 0.22 (1-.22)/10120.013
• Margin of error 2 (0.013) 0.026
• Interval is 22 2.6

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Crime in own neighborhood

• Only 3 thought crime was extremely serious in
  their own neighborhood.
• s.d.sqrt (0.03)(0.97)/10120.0053
• Margin of error 2(0.0053)0.016, or 1.6
• Confidence interval is 3 1.6