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STAT 135 LAB 10

STAT 135 LAB 10. Learning Objective # 67 TA: Dongmei Li. A Story.

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STAT 135 LAB 10

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  1. STAT 135 LAB 10 Learning Objective # 67 TA: Dongmei Li

  2. 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?

  3. 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 isn’t way better than the others, the average of all 50 should be more reliable.

  4. 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.

  5. 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.

  6. 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).

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