Lec7 - Turn to your neighbor and define the sampling...

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Turn to your neighbor and … - define the sampling distribution of Y - describe how sample size affects this distribution -
Image of page 1

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

View Full Document Right Arrow Icon
Confidence intervals: Locating an invisible man! The man is within 2 SE’s of the dog about 95% of the time We know where the dog is, and we’d like to estimate where the man is. We know that 95% of the time the man is within 2 SE’s of the dog, so we say that we are 95% confident that the man is in this interval. y y μ μ μ y μ μ 95% confidence interval
Image of page 2
Confidence intervals: Mathematically RECALL: If Y has a normal distribution, then Y has a normal distribution. Pr{ 1.96 < Z < 1.96} = .95 (Almost, but not exactly two standard deviations.) Start with the standardized scale: Use the Z table to figure out what we add and subtract from the mean to get 95% of the distribution. y ± 1.96 σ n Therefore, the interval will contain μ for 95% of all samples. RECALL: The standard deviation of the sampling distribution of is Y σ n . Pr{ Y 1.96 σ < μ < Y + 1.96 σ } = .95 So for any normal distribution: Pr{ μ 1.96 σ < Y < μ + 1.96 σ } = .95 μ + 1.96 σ μ 1.96 σ
Image of page 3

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

View Full Document Right Arrow Icon
BUT, we don’t necessarily know σ If the data come from a normal population, then we can use s to estimate σ , but then we have to change the multiplier from 1.96 to something else in order to estimate the 95% confidence interval. y ± 1.96 σ n Therefore, the interval will contain μ for 95% of all samples. W.S. Gosset (1876-1937), Guinness Brewery, 1908, ‘Student’
Image of page 4
BUT, we don’t necessarily know σ If the data come from a normal population, then we can use s to estimate σ , but then we have to change the multiplier from 1.96 to something else in order to estimate the 95% confidence interval.
Image of page 5

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

View Full Document Right Arrow Icon
Image of page 6
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