Large large enough for the normal approximation to be

Info icon This preview shows pages 130–132. Sign up to view the full content.

View Full Document Right Arrow Icon
large (large enough for the normal approximation to be valid), we saw that these confidence intervals have a very convenient form: statistic + margin-of-error where margin-of-error = critical value × standard error of statistic. The critical value is the number of standard errors you want to use corresponding to a specified confidence level. Keep in mind that the level of confidence provides a measure of how reliable the procedure will be in the long-run (which can vary by procedure and sample conditions). Finally, you saw that this reasoning process holds equally well when the sampling is from a finite population, where the randomness in our model comes from the selection of the observational units, not in the observational units’ individual outcomes. Here we took a bit more care to convince ourselves that the sample will be representative of the larger population. This is done by using random mechanisms to
Image of page 130

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Chance/Rossman, 2015 ISCAM III Chapter 1 Summary 130 select the sample. These random mechanisms (e.g., simple random sampling) lead to samples that will generally have characteristics mirroring those of the larger population. Although random sampling prevents systematic sampling errors, you still need to worry about non-sampling errors (e.g., wording of a question). Also, there will still be random sampling variability the characteristics of the sample will vary from sample to sample. Technically we should use the hypergeometric distribution to model the behavior of the statistic. But we saw that if the population is large compared to the size of the sample (e.g., more than 20 times larger), then we can use the same binomial distribution and if the sample size is also large we can use normal-based methods to determine p-values and confidence intervals (as well as power and sample size calculations). The interpretation of the p-value is essentially the same but now applies to the randomness inherent in the sampling process. Also keep in mind that the confidence interval aims to capture the proportion of the population having the characteristic of interest. (Note, when the population is large, these are actually equivalent because the probability of any one randomly selected observational unit being a success will equal the population proportion of successes and we are approximating this as constant for every member of the sample.) SUMMARY OF WHAT YOU HAVE LEARNED IN THIS CHAPTER x The reasoning process of statistical inference x The terms parameter to describe a numerical characteristic of a population or process and statistic to describe a numerical characteristic of a sample x The symbol S to represent the probability of success for a process or the population proportion and p ˆ to represent a sample proportion of successes x The fundamental notion of sampling variability and how to simulate empirical sampling (null) distributions “by hand” (e.g., using cards) and using technology (e.g., with an applet) x How to estimate and interpret a p-value x
Image of page 131
Image of page 132
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern