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Confidence Intervals

Confidence Intervals. The following was taken from a recent obesity survey conducted by the CBC.

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Confidence Intervals

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  1. Confidence Intervals • The following was taken from a recent obesity survey conducted by the CBC. • “The online poll of 1,514 adults and 506 youth aged 12 to 17 was conducted by Leger Marketing from Nov. 10 to Nov. 17, 2010. The margin of error for the adult sample is plus or minus 2.5 percentage points, 19 times out of 20, and plus or minus 4.4 percentage points, 19 times out of 20 for youth.” • Read more: http://www.cbc.ca/health/story/2010/12/31/canada-weighs-in-poll-health-myths.html#ixzz19zcOhCSf

  2. Interpretation • “plus or minus 2.5 percentage points, 19 times out of 20” • This means that 95% of the time that a poll of this size is done, the result will be within a range that is at most 2.5% off. • Only 5% of the time the poll will be more than 2.5 % off.

  3. Calculating a Confidence Interval • Once we have establishes our significance level α we can establish the range of values where the mean is likely to be (with probability 1- α) using the formula below.

  4. The variables: n and σ are the sample size and population standard deviation as always.

  5. Z-Score Explanation • To be 95% sure that the mean is in the given range, we must be 97.5% sure it is not over and 97.5% sure it is not under. • If there is a 5% chance of error, there is a 2.5% chance of OVER ESTIMATING and a 2.5% chance of UNDER ESTIMATING. • That is why we use 97.5% to be 95% confident.

  6. Example: Light Bulbs • You manufacture light bulbs and know that their lifespan has a standard deviation σ=10.5 hours. • You have Tested 25 bulbs with continuous use and found that bulbs in your sample last on average 106 hours. • How long can you claim that they last with 95% confidence?

  7. The 95% Confidence Interval • 106-(1.96)(10/ √25) < µ < 106+(1.96)(10/ √25) • 102.08 < µ < 109.92 • Note: 1.96 is the Z –Score that goes with 97.5% for our 95% confidence interval.

  8. A Fare Claim • It would be fair to that the bulbs last 100 hours. • We are 97.5% sure that each individual bulb will last at least 102.08 hours.

  9. Range of Proportions: When it is a proportion of the population, not a value that you are measuring, the confidence interval takes this form. is the measured proportion expressed as a percentage.

  10. practice • Page 464 • Questions 3, 4,5, 6,7

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