STAT 135 LAB 10

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STAT 135 LAB 10

• Learning Objective 67
• TA Dongmei Li

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A Story

• The most accurate clock in the world is the
  NIST-F1 built by the National Institute of
  Standards and Technology in Boulder Colorado. It
  is an atomic clock that is accurate to a tenth of
  a nanosecond (it might lose a second in 20
  million years). Coordinated Universal Time (UTC)
  is the official world time. UTC is a weighted
  average of 250 different atomic clocks in 50
  countries.
• Question why not just use the best clock
  (NIST-F1) to set the official world time?

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Answer to above question

• Because the average of many independent
  measurements is more reliable than a single
  measurement using the same process. Thus, as long
  as that clock isnt way better than the others,
  the average of all 50 should be more reliable.

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THE LAW OF AVERAGES

• More independent trials
• Averages or proportions are likely to be more
  stable.
• The margin of error will decrease.
• However, sums or counts are likely to be more
  variable when the number of independent trials
  increases.

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Example

• Flip a coin 10000 times. Have 5069 heads.
• The proportion of getting heads is more stable in
  this case
• Flip a coin 1000 times. Have 525 heads.
• The variability of number of heads in 1,000
  trials is much less than the variability of
  number of heads in 10,000 trials.

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Learning objective for Lab 10

• 67. As the number of independent repetitions of a
  random phenomenon increases, the relative
  frequency of a particular event tends to get
  closer and closer to its probability. However the
  number of times that the event occurs will tend
  to depart more and more from what is expected
  (i.e., the number of repetitions times the
  probability).