Description

Reviews

• Chapter 1: Picturing Distributions with Graphs • Chapter 2: Describing Distributions with Numbers • Chapter 3: The Normal Distributions

• 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

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

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: