{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chapter9_STAT1100.ppt", filename="Chapter9_STAT1100.ppt", filename="Chapter9_STA

Chapter9_STAT1100.ppt", filename="Chapter9_STAT1100.ppt", filename="Chapter9_STA

Info icon This preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
Sampling Distributions Statistics for Management and Economics Chapter 9
Image of page 1

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

View Full Document Right Arrow Icon
Objectives Sampling Distribution of the Mean Sampling Distribution of a Proportion Sampling Distribution of the Difference Between Two Means
Image of page 2
Sampling Distributions… A sampling distribution is created by, as the name suggests, sampling . The sampling distribution of a statistic is the distribution of all possible values taken by the statistic when all possible samples of a fixed size n are taken from the population. It is a theoretical idea— we do not actually build it. The sampling distribution of a statistic is the probability distribution of that statistic. The method we will employ on the rules of probability and the laws of expected value and variance to derive the sampling distribution. Recall: statistic describes the sample, parameter describes the population!
Image of page 3

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

View Full Document Right Arrow Icon
The law of large numbers Law of large numbers : As the number of randomly drawn observations ( n ) in a sample increases, the mean of the sample ( ) gets closer and closer to the population mean μ (quantitative variable). the sample proportion ( ) gets closer and closer to the population proportion ρ (categorical variable). x ˆ p
Image of page 4
Sampling distribution When sampling randomly from a given population, the law of large numbers describes what happens when the sample size n is gradually increased. The sampling distribution describes what happens when we take all possible random samples of a fixed size n . Sampling distribution of [ insert statistic here ]
Image of page 5

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

View Full Document Right Arrow Icon
Sampling distribution of x bar (the sample mean) We take many random samples of a given size n from a population with mean μ and standard deviation σ . Some sample means will be above the population mean μ and some will be below, making up the sampling distribution.
Image of page 6
Sampling distribution of x bar Sampling distribution of x bar μ σ / n For any population with mean μ and standard deviation σ : The mean, or center of the sampling distribution of x bar, is equal to the population mean μ . The standard deviation of the sampling distribution is called the standard error , and defined as σ /√ n , where n is the sample size.
Image of page 7

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

View Full Document Right Arrow Icon
Sampling distribution of x bar Mean of a sampling distribution of x bar: There is no tendency for a sample mean to fall systematically above or below μ, even if the distribution of the raw data is skewed. Thus, the mean of
Image of page 8
Image of page 9
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