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Unformatted text preview: Confidence intervals Two populations: means Two populations: proportions Inference Review : Outline • Confidence intervals for population parameters • Inference for population parameters in two samples • Two means • Two proportions T. Parker () 1 / 19 Confidence intervals Two populations: means Two populations: proportions Confidence Intervals • Similar procedure to the way that we found test statistics above. • Generally, if a statistic T has expectation μ T and standard error se T , we will use the formula T ± cv α/ 2 se T where cv α/ 2 is some critical value. 1 α is the confidence level associated with the interval. • There’s no hypothesis, so a hypothesized μ T isn’t here! • How is this related to the hypothesis tests before? T. Parker () 2 / 19 Confidence intervals Two populations: means Two populations: proportions A picture using the normal distribution Theoretically, what is going on: standard normal dist. z z α 2 z 1α 2 using the sample mean x x z α 2 σ n x x + z 1α 2 σ n • Same procedure with the t distribution. T. Parker () 3 / 19 Confidence intervals Two populations: means Two populations: proportions Example Coffee shop again: from your collection of revenue data — 60 coffee shops, with an average of $840,000 and population standard deviation of $20,400 — what is a 95% confidence interval for the mean revenue of all coffee shops in the midwest? • What is different if the standard deviation was estimated from the sample? • How is this related to the hypothesis test from before? Normal table t table T. Parker () 4 / 19 Confidence intervals Two populations: means Two populations: proportions Example A newspaper poll of 250 people found that 180 of them think the United States is currently in a recession. What is a 90% confidence interval for the population proportion of people with the opinion that the US is in a recession?...
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This note was uploaded on 09/26/2011 for the course 06E 071 taught by Professor Stuff during the Spring '11 term at University of Iowa.
 Spring '11
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