4-intro - 4 Statistical Inference Sampling Distribution...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
§ 4. Statistical Inference: Sampling Distribution, Confidence Intervals, and Tests of Hypotheses This chapter is the central part of the statistics course. It contains the two main topics: confidence intervals hypotheses testing We will do these for a few types of parameters/distributions. In addition, we will also discuss the choice of sample size and maybe a few other issues. The remaining two chapters on the syllabus discuss other situations (linear regression and Analysis of Variance, abbreviated ANOVA). There is a basic idea in all these. Once we understand the approach, the rest is just working out (or, for now, digesting) the “gory details”. The rest of these notes contains parts of §§ 4.1.1, 4.1.2, 4.1.3 and the intro to 4.2. CI. Confidence intervals (abbreviated CI) We will introduce the general approach on a case that is most straightforward. CI.1. Estimating the mean μ in a normal distribution, when the standard devi- ation σ is known. We need the following: As . assumptions Es . design an experiment, find a statistics (also called “estimator”) Ds . figure out the distribution of the estimator (given the assumptions) CI . using Ds , and the random sample that we drew, compute the CI Let’s take them one at the time: 1
Image of page 1

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

View Full Document Right Arrow Icon
As. The assumptions Let us say that we have the following situation. We manufacture on a machine in our factory balls. We would like to estimate the average diameter. From previous measurements we know that the standard deviation is σ = 0 . 01 in. We adjusted the machine, and we would like to see what (average) diameter the produced balls have.
Image of page 2
Image of page 3
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