ch17thet-coefficientandthet-test.studentview

ch17thet-coefficientandthet-test.studentview - Chapter17...

Info icon This preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Chapter 17:  The  t -Coefficient and the  t -Test A. Introduction In the previous two chapters, we studied inferences on  μ when (i) the population is normal and (ii) the standard deviation σis known. However, the assumption that σis known is NOT practical as we do not even know the μ. That we assumed σis known was mainly for the preliminary discussions in the earlier chapters, which acted as a stepping stone for a more in-depth study in this and the following sections. Note : We also assume ( and ALWAYS assume) that are random and independent. n x x x , , ......... , 2 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
Question What shall we do if  σis really UNKNOWN? Answer It turns out that two slight modifications will lead to  adequate statistical inference procedures for  μ. These will be discussed below. First modification : Replace the unknown σ by its point estimate: This estimate was discussed in Chapter 14(C). 1 . . , 1 ) ( 2 - = - - = n f d n x x s i
Image of page 2
Second modification Replace the  z -coefficient or  z -critical value by a  so-called  t -coefficient  or  t-critical value , taken  from a  t-table . (Table7). The  t-distribution  was invented in 1908 by an English  statistician named  William Sealy Gosset  (1876-1937). He was a researcher at Guinness Brewery. He invented the student t-distribution to handle small samples  in quality control in brewing.  The company forbade the publication of research by its  employees. So, he published his famous results in the pen- name “Student”  (meaning, that he was a humble student of  Karl Pearson  and  Ronald Alymer Fisher  who published articles in  Biometrika  -a scientific journal that principally covers  theoretical   statistics) Thus, the  t- distribution is also called the  Student t- distribution.
Image of page 3

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

View Full Document Right Arrow Icon
         Gosset                                                Fisher Pearson
Image of page 4
Image of page 5
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