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STA291

STA291. Statistical Methods Lecture 18. Last time…. Confidence intervals for proportions. Suppose we survey likely voters and ask if they plan to vote for Measure A. Of the 516 people selected at random, 289 say they would vote for the measure.

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STA291

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  1. STA291 Statistical Methods Lecture 18

  2. Last time… • Confidence intervals for proportions. • Suppose we survey likely voters and ask if they plan to vote for Measure A. Of the 516 people selected at random, 289 say they would vote for the measure. • A) Construct and interpret a 99% confidence interval for the true proportion of voters who will vote for Measure A. • B) What sample size should we use if we want a confidence interval that’s plus or minus 3% assuming worst case scenario?

  3. A natural starting point: What about ? Thanks to the CLT … We know is approximately normal with mean and standard deviation ___ and ____, respectively.

  4. Estimation of a Mean The sample mean is an unbiased and efficient point estimator of the population mean m.

  5. Confidence Interval for a Mean • A large sample confidence interval for the population mean mwould have the form • where is the sample mean, s the population standard deviation

  6. Stuck with the Sample Standard Deviation? Confidence intervals are constructed in the same way as before, but now we are using t-values instead of z-values Speak of the distribution’s degrees of freedom, usually abbreviated df or n (“nu”), equal to the sample size minus 1[n = n – 1].

  7. t-Distributions

  8. Confidence Interval for a Mean, Unknown Population Standard Deviation • For a random sample from a normal distribution, the confidence interval for m is • where tn-1 is the appropriate t-score (instead of z-score) for the desired level of confidence

  9. Sample size calculation • Suppose we’re given a target bound on our margin of error, ME • This can be solved for the sample size, n: • But wait, why z…

  10. Looking back • Estimation of means • Point estimate • t-distribution • properties • when to use • Confidence interval estimate • assumptions • interpretation • Sample size calculation

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