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Chapter 3

STA 200 Summer I 2011. Chapter 3. Example. In 2007, Zogby conducted a poll regarding space. 13% of 2841 American adults surveyed believed regular commercial travel to space will exist by 2020. What percentage of all American adults believe this?

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Chapter 3

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  1. STA 200 Summer I 2011 Chapter 3

  2. Example • In 2007, Zogby conducted a poll regarding space. • 13% of 2841 American adults surveyed believed regular commercial travel to space will exist by 2020. • What percentage of all American adults believe this? • We know the percentage in the sample, we estimate the percentage in the population.

  3. Parameters • A parameter is a number that describes the population. • A parameter is a fixed number, but we usually don’t know it’s true value. • In the example, the parameter is:

  4. Statistics • A statistic is a number that describes a sample. • The value of a statistic will be known after data is collected from a sample. • In the example, the statistic is 13%.

  5. Parameters and Statistics • Notation: • Population proportion (parameter): p • Sample proportion (statistic): • We use statistics to estimate unknown population parameters.

  6. Example • The Gallup Organization conducted a poll last month relating to the economy. 18,850 American adults were surveyed, and 9.4% of them were unemployed. • Determine the population, sample, parameter, and statistic.

  7. Bias and Variability • When using a statistic to estimate a parameter, there are 2 possible errors: bias and variability.

  8. Bias • Bias is consistent, repeated deviation of from p when many samples are taken. • Bias is significantly reduced by using a good sampling method (like simple random sampling).

  9. Variability • Suppose Zogby takes another sample of 2841 American adults. Will they get the same statistic as before? • Even if we use a good sampling method, we’ll get different statistics for different samples. • The idea that the value of a statistic will vary from one sample to another is called sampling variability.

  10. Variability (cont.) • Variability is a measure of how spread out the values of a statistic are when many samples are taken. • It can be reduced by taking a larger sample.

  11. Margin of Error • From the space travel poll: • “…the margin of error with 95% confidence is +/- 1.9 percentage points.” • This means: If we took all possible samples using the same method used to get the one in the poll, 95% of them would yield a within 1.9 percentage points of p. • In practice, only one sample is taken.

  12. Step by Step • Usually, won’t be equal to p. • The margin of error gives us an idea of how close is to p. • We can’t be certain (100% confident) that is within 1.9 percentage points of p.

  13. Step by Step (cont.) • There’s no way to determine if the sample is one of the 95% yielding a within 1.9 percentage points of p, or one of the other 5%.

  14. Confidence Statements • Consist of the margin of error and confidence level. • Concern what happens in all possible samples. • Always apply to the parameter.

  15. Confidence Statements (cont.) • We can use other confidence levels besides 95%. As confidence level increases, margin of error increases. • If you want a smaller margin of error, use a larger sample. • If the confidence level is not given, assume 95% confidence.

  16. Example • In a CBS News poll of 240 parents of K-12 children, 58% believed their children are getting a better education than they did. • Determine the (a) population, (b) sample, (c) parameter, and (d) statistic.

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