STA291

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