helpsession_module6_S18.pdf

helpsession_module6_S18.pdf - PHC 4069 Biostatistics in...

Info icon This preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
PHC 4069 Biostatistics in Society Module 6 Help Session Sampling distributions for sample statistics Prepared by: Hanze Zhang Presented by: Ying Ma
Image of page 1

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

View Full Document Right Arrow Icon
Sampling distribution of a sample statistic What is is: the probability distribution for the values of the sample statistic based on a random sample that exhibits random sampling variation among repeated samples taken from the same population What it shows: Range of possible values for the sample statistic Probabilities associated with each of these values or with a range of values Ex: sampling distribution of the mean weight in a population of university students.
Image of page 2
Sample proportion p Example: What proportion (P) of USF students have blond hair? In order to find out: Obtain a random sample of n USF students (Random phenomenon) Determine for each student in the sample if they do or do not have blond hair (Yes or no), in other words... Count the number of students (X) who have blond hair in the sample of n USF students (Binomial random variable) Compute the sample proportion p=X/n ^ ^ ^
Image of page 3

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

View Full Document Right Arrow Icon
Sample proportion p The sample proportion p is an estimate of P = true population proportion This is directly related to the count X (binomial random variable) p=X/n ^ ^ ^
Image of page 4
Sample proportion p In module 5: the probability distribution for X=number of hispanic students in a sample of n=3 students The sample space for the count X: {0, 1, 2, 3} (discrete) The sample space for p (X/n): {0, 0.33, 0.67, 1.0} As the sample size (n) increases, the values of p look more like a continuous variable, with a range of 0 to 1.0 Ex: with n=100 the sample space for p (X/n): {0.01, 0.02, ... 0.99, 1.0} ^ ^ ^ ^
Image of page 5

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

View Full Document Right Arrow Icon
From last week’s help session:
Image of page 6
Sample proportion p Lecture 6.1: Sampling Distribution for Proportion of “Heads” Out of 10 Coin Tosses ^ 0 0.05 0.1 0.15 0.2 0.25 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sample Proportion P [X]
Image of page 7

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

View Full Document Right Arrow Icon
Sample proportion p From last week’s help session: the normal distribution curve for continuous variables ^
Image of page 8
Normal approximation to a binomial distribution If the sample size is sufficiently large, the sampling distribution of p becomes approximately normal : If n P ≥ 10 and n(1 P ) ≥ 10 Center”: E( p ) = P “Spread”: σ p = 𝑃(1−𝑃) 𝑛 E( p ) is the expected value of the sample proportion, p , and P is the proportion in the underlying population ^ ^ ^
Image of page 9

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

View Full Document Right Arrow Icon
Normal approximation to a binomial distribution (lecture 6,2) From lecture 6.2: 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0 0.1 0.2 0.3 0.4 0.5 Sample Proportion P [X] Binomial (n=10, P=0.1) Normal (μ=0.1, σ=0.095)
Image of page 10
Image of page 11
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