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UO / Mathematics / MATH 243 / What is a density curve?

What is a density curve?

What is a density curve?

Description

School: University of Oregon
Department: Mathematics
Course: Introduction to Methods of Probability and Statistics
Professor: Harker h
Term: Fall 2015
Tags:
Cost: 50
Name: Midterm 1 Study Guide
Description: It has lots of pictures!
Uploaded: 10/26/2015
8 Pages 178 Views 2 Unlocks
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• Chapter 1: Picturing Distributions with Graphs  • Chapter 2: Describing Distributions with Numbers  • Chapter 3: The Normal Distributions  


What is a density curve?



• Chapter 8: Producing Data: Sampling  • Chapter 9: Producing Data: Experiments  • Chapter 12: Introducing Probability  

• Chapter 15: Sampling Distributions  

• Chapter 16: Confidence Intervals: The Basics  • Chapter 17: Tests of Significance: The Basics  • Chapter 18: Inference in Practice  

• Excel Functions  

• Histogram

• Box Plots  

• Stemplots


What is the difference between population distribution and sampling distribution?



Don't forget about the age old question of What is moore's law all about?

• Bar Graphs  

• Pie Charts

• Calculate the median and mean (average) of a set of observations  

◦Mean (average): add up all numbers and divide by how many numbers in a data set  


Suppose our population disstribution is n (μ, 60). a sample of 18 workers gives x̄ =17. they prefer self-paced on average. is this good evidence against h0?



Don't forget about the age old question of What is a measure of thunderstorm potential based on vertical temperature lapse rate, moisture content of the lower atmosphere, and vertical extent of the moist layer?

• 5-number summary  

◦First quartile: average of the first half of the numbers (not including the median)  ◦Third quartile: average of the last half of the numbers (not including the median)  

• Normal distributions N(μ,σ), standard Normal distribution N(0,1), Normal distribution of a  sample N(μ,σ/√n)  We also discuss several other topics like What are the three doric layers of entablature?

Normal distribution N(0,1)

• shape of a distribution: skewed right, skewed left, symmetric  

◦skewed right:  

◦skewed left:  

◦symmetric: bell-shaped curve  

• What is a density curve?  

If you want to learn more check out What is a type of rock that is granite, basalt, gabbro?

• Calculate proportion of observations from a Normal distribution using table A  

• z-scores  

◦z=(x-μ)/σ

◦(x = μ + zσ)  Don't forget about the age old question of What are the economic, social, and political characteristics of developing countries?

• 68-95-99.7 rule  

◦approximations  

• Terminology about sampling (population, sample, simple random sample (SRS), bias, etc.)  ◦population: an entire group of individuals  

◦sample: part of the population from which we collect information  

◦simple random sample (SRS): SRS of size n consists of n individuals from the population  chosen in such a way that every set of n individuals has an equal chance to be the sample  actually selected  

◦bias: when an outcome is favored  

◦sample design: describes exactly how to select a sample from a population  ◦convenience sample: taking members from a population that are easiest to reach

◦voluntary sample: consists of people who choose themselves by responding to broad  appeal  We also discuss several other topics like What are the circumstances of invasion of privacy?

• Terminology about experiments and observational studies (treatments, subjects, factors,  matched pairs, control, randomization, etc.)  

◦treatments: any specific experimental condition applied to the subjects  

◦subjects: individuals in an experiment  

◦factors: explanatory variables  

◦matched pairs: A matched pairs design compares two treatments. Choose pairs of subjects  that are closely matched as possible. Use chance to decide which subject in a pair gets the  first treatment. Sometimes each "pair" in a matched pairs design consists of just one  subject who gets both treatments. The order of the treatments is randomized.  ◦control: something that other things can be compared to  

◦randomization: used to decrease bias  

◦statistically significant: when an observed effect so large that it would rarely occur by  chance  

• Sample spaces, discrete and continuous probability models  

◦sample space: the set of all possible outcomes in a random phenomenon  ◦discrete probability models: a probability model with a finite sample space (each outcome  is given a probability and the sum of those probabilities is 1)  

◦continuous probability models: assigns probabilities as areas under a density curve. The  sample space is a range of values  

‣ Example: Let X be a randomly chosen number between 0 and 1  

• S= {all numbers between 0 and 1}  

• S={X|0<X<1}  

• calculate probabilities: in a discrete probability distribution AND in a continuous probability  distribution like heights of men  

• Population distributions and sampling distributions (and their relationship)

• Central Limit Theorem  

• give confidence intervals for different confidence μ (with known σ) (x ± z √n ) and understand the margin of error and how to change its size.  

• understand how to compute critical values (z∗) for different confidence levels.

• Understand Null and Alternative Hypotheses  

◦Null Hypothesis: the claim tested by a statistical test  

◦Alternative Hypothesis: the claim that we're trying to find evidence for

• calculate P-values and perform z tests for a population mean  

• describe P-values relative to significance levels α (alpha)  

SAMPLE PROBLEM:

 

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