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

# What is a density curve? Description

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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?  • Bar Graphs  If you want to learn more check out What new media object can be transcoded into different formats?

• 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?
If you want to learn more check out In basic building elements, what is typically used for foundation walls?

• 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) Normal distribution N(0,1) • shape of a distribution: skewed right, skewed left, symmetric  Don't forget about the age old question of What is the density of the asthenosphere?

◦skewed right:

◦skewed left:

◦symmetric: bell-shaped curve

• What is a density curve? • Calculate proportion of observations from a Normal distribution using table A

• z-scores

◦z=(x-μ)/σ

◦(x = μ + zσ)

• 68-95-99.7 rule

◦approximations • Terminology about sampling (population, sample, simple random sample (SRS), bias, etc.)  ◦population: an entire group of individuals  We also discuss several other topics like What are the economic, social, and political characteristics of developing countries?

◦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  Don't forget about the age old question of Define tort.

• 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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