This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Stats Study Guide Exam 4 Chapter 18: Inference about a Population Mean Online Notes Here are the conditions needed for realistic inference about a population mean: CONDITIONS FOR INFERENCE ABOUT A MEAN We can regard our data as a simple random sample (SRS) from the population. This condition is very important. Observations from the population have a Normal distribution with mean and standard deviation . In practice, it is enough that the distribution be symmetric and singlepeaked unless the sample is very small. Both and are unknown parameters. Because is unknown, STANDARD ERROR When the standard deviation of a statistic is estimated from data, the result is called the standard error of the statistic. The standard error of the sample mean is s / n . And THE ONESAMPLE t STATISTIC AND THE t DISTRIBUTIONS has the t distribution with n 1 degrees of freedom. Degrees of freedom : there is a different t distribution for each sample size. We specify a particular t distribution by giving its degrees of freedom. (n 1 in for t distributions) Differences b/w t distribution density curve and a normal curve The density curves of the t distributions are similar in shape to the standard Normal curve. They are symmetric about 0, singlepeaked, and bellshaped. The spread of the t distributions is a bit greater than that of the standard Normal distribution . The t distributions in Figure 18.1 have more probability in the tails and less in the center than does the standard Normal. This is true because substituting the estimate s for the fixed parameter introduces more variation into the statistic . As the degrees of freedom increase, the t density curve approaches the N (0,1) curve ever more closely. This happens because s estimates more accurately as the sample size increases. So using s in place of causes little extra variation when the sample is large. o THE ONESAMPLE t CONFIDENCE INTERVAL Stats Study Guide Exam 4 Draw an SRS of size n from a large population having unknown mean . A level C confidence interval for is where t * is the critical value for the t ( n 1) density curve with area C between t * and t * ....
View Full
Document
 Fall '08
 Chizmar
 Economics

Click to edit the document details