Lecture_20,_Chap_10,_Sec_2a

Lecture_20,_Chap_10,_Sec_2a - Chapter 10 Section 2 Testing...

Info icon This preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
Chapter 10 Section 2 Testing Claims about a Population Mean Assuming the Population Standard Deviation is Known
Image of page 1

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

View Full Document Right Arrow Icon
Hypothesis Test for Mean – σ Known Learning objectives Understand the logic of hypothesis testing Test a claim about a population mean with σ known using the classical approach Test a claim about a population mean with σ known using P -values Test a claim about a population mean with σ known using confidence intervals Understand the difference between statistical significance and practical significance 1 2 3 5 4
Image of page 2
Logic of Hypothesis Testing We have the outline of a hypothesis test, just not the detailed implementation How do we quantify “unlikely”? How do we calculate Type I and Type II errors? What is the exact procedure to get to a do-not- reject / reject conclusion?
Image of page 3

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

View Full Document Right Arrow Icon
Logic of Hypothesis Testing There are three equivalent ways to perform a hypothesis test They will reach the same conclusion The methods are The classical approach The P -value approach The confidence interval approach
Image of page 4
Logic of Hypothesis Testing The classical approach If the sample value is too many standard deviations away, then it must be too unlikely If the sample value is too many standard deviations away, then it must be too unlikely The P -value approach If the probability of the sample value being that far away is small, then it must be too unlikely The confidence interval approach If we are not sufficiently confident that the parameter is likely enough, then it must be too unlikely Don’t worry … we’ll be explaining more
Image of page 5

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

View Full Document Right Arrow Icon
Logic of Hypothesis Testing The three methods all begin the same way We have a null hypothesis, that the actual mean is equal to a value μ 0 We have an alternative hypothesis We have a null hypothesis, that the actual mean is
Image of page 6
Logic of Hypothesis Testing The three methods all need information We run an experiment We collect the data We calculate the sample mean We run an experiment We collect the data We calculate the sample mean The three methods all make the same assumptions to be able to make the statistical calculations That the sample is a simple random sample That the sample mean has a normal distribution
Image of page 7

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

View Full Document Right Arrow Icon
Logic of Hypothesis Testing In this section we assume that the population standard deviation σ is known (as in section 9.1) We can apply our techniques if either The population has a normal distribution, or Our sample size n is large ( n ≥ 30) In those cases, the distribution of the sample mean is normal with mean μ and standard deviation σ / √ n x
Image of page 8
Logic of Hypothesis Testing The three methods all compare the observed results with the previous criterion
Image of page 9

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

View Full Document Right Arrow Icon
Image of page 10
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