Sampling Distributions and Confidence Intervals: Understanding the Basics, Lecture notes of Probability and Statistics

Download Sampling Distributions and Confidence Intervals: Understanding the Basics and more Lecture notes Probability and Statistics in PDF only on Docsity! "Big Picture" Questions & Answers 1. What is the sampling distribution of the sample mean? It is the probability distribution of the sample mean from a random sample of a particular size (n) taken from some population. It is best visualized by thinking of computing the sample mean for a sample of size n, and then repeating this step many times to produce many sample means, and now think of the density function which describes the relative frequencies of the various possible values for these sample means. 2. Why is it useful? It is useful because it describes how far the sample mean might be from the population mean, and it is the population mean we are usually interested in. 3. What is a sampling distribution (more generally)? In the description at 1. above, just replace "sample mean" by "statistic". Recall that a statistic, in general, is just a function of the all the sample values (in a random sample of size n). Usually we construct a statistic so that it will be an estimator of a parameter. 4. What are parameters? Parameters are characteristics (usually numeric) of a population. They are usually the values that we try to estimate based on our sample data. 5. Why do we want estimates of parameters? The "population" in these discussions is the group of numbers we want to know something about. e.g. the voting intentions of the electorate, the SFU student body, the stars in the sky over magnitude .1... 6. Why are point estimates not very useful? An estimate of a parameter is not very reliable information unless it is reasonably precise – that is, unless the estimate has an acceptable standard deviation. So we need an estimate of precision to make point estimates more useful. 7. How do we provide more useful estimates? ...By using interval estimates, such as Confidence Intervals. 8. What determines the technique for CIs? The question has an answer if we restrict our attention to CIs for the population mean. Then the determinants are the sample size, whether the population distribution is normal, and whether the population SD is known or not. 9. Why are proportions and averages treated similarly? Because a proportion can be understood to be an average. 10. Why are proportions and averages treated differently?