Chapter6 - 6.1 confidence interval for population mean...

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1 Chapter 6 Introduction to Inference (covered by about 4 lectures) 6.1 confidence interval for population mean • Example 1: mean SATM score for seniors in California CI - interpretation Woops, missed
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2 Example 2: confidence level effect Example 2: sample size effect Length of confidence interval • The length of CI depends on how certain we want to be (smaller confidence level, shorter CI) • Increase the sample size n will shrink the CI, because Intuition: More data lead to more accurate estimate of the true parameter. • Smaller leads to smaller CI (experimental or sampling design) X X n
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3 Confidence interval - Caveats • The data must be a random sample from the population (for the formula we learned). – Random: sampling errors come from chance variation, and they die down as the sample size increases. – Non-random sample: systematic errors could dominate sampling errors, and they do not fade away as the sample size increases. • Outliers can have a large effect on the CI. •I f n is small then you need X to be normal . If n>15 , then underlying distribution can often be different from normal and the sample mean will still be close to normal. Concluding remarks 95% confidence interval does say : – Among all possible samples, the interval will cover the population mean for 95% of the time. – Note that this interval varies from sample to sample. 95% confidence interval does NOT say : – For 95% of probability, the CI computed from a specific sample has contained the population parameter. 1.96 , 1.96 XX nn      6.2 Significance Testing What is hypothesis? • A tentative explanation for a phenomenon, used as a basis for further investigation. • It could be either right or wrong.
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4 Hypothesis – an example For hundreds of years it was assumed that the sun revolved around the earth . The fact that the sun appears to rise in the east every morning
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Chapter6 - 6.1 confidence interval for population mean...

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