{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ecn10-lecture13-v1

ecn10-lecture13-v1 - Economics 10 Introduction to...

Info icon This preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Economics 10: Introduction to Statistical Methods Statistical Inference
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
Overview of Inference Methods for drawing conclusions about a population from sample data are called statistical inference Methods Confidence Intervals - estimating a value of a population parameter Tests of significance - assess evidence for a claim about a population Inference is appropriate when data are produced by either a random sample or a randomized experiment
Image of page 2
Confidence Intervals
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
Today: Confidence Intervals The confidence interval is a range of values with an associated probability or confidence level C . The probability quantifies the chance that the interval contains the true population parameter. Using a sample to estimate a population parameter – Estimate will be somewhat different than the true population parameter by chance (sampling variability). Can we be more informative than “somewhat different”? Ask: what interval can we say contains μ X C % of the time? Ex: what interval contains μ X 95 % of the time? A confidence interval σ is known Special case: polling – conservative bounds σ is unknown – t-distribution
Image of page 4
When is ? When SRS + Any time the data are drawn from a normally distributed population Linear functions of normally distributed random variables are also normally distributed When SRS + large n Central Limit Theorem ( 29 2 , ~ X X i N X σ μ n N X X X 2 , ~ σ μ SRS = simple random sample
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
Review: standardizing the normal curve using  z N (0,1) z x N (64.5, 2.5) N ( µ , σ /√ n ) Standardized height (no units) z = x - μ σ n Here, we work with the sampling distribution, and σ /√ n is its standard deviation (spread). Remember that σ is the standard deviation of the original population.
Image of page 6
68-95-99.7% Rule Rule of thumb for areas under a normal ≈68% of values within 1 s.d. of the mean ≈95% of values within 2 s.d. of the mean ≈99.7% of values within 3 sd of the mean Implications for the sample mean ≈68% of estimates on interval
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
Image of page 8
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