Stats 201 Week 4 Notes
Stats 201 Week 4 Notes STAT 201
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This 2 page Class Notes was uploaded by AlliSlaten on Monday September 19, 2016. The Class Notes belongs to STAT 201 at Colorado State University taught by Kirk Ketelsen in Fall 2016. Since its upload, it has received 11 views.
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Date Created: 09/19/16
- Random Events - Random event- something that may or may not occur, and that which we can assign probability to - Random Variable- generally denoted as “x”, which is a possible value - Complement- is its non-occurance, or its opposite - EX. Flip a coin and it comes up tails - Probability - Probability- way of quantifying the likelihood (chance) that some random event occurs - EX. if there’s a 50% chance of happening the probability is 0.5 - Probability is between 0 and 1 - Relative Frequency - Relative frequency- expresses how often an event occurs as a proportion of how often it potentially could have occurred - The “relative frequency” interpretation of probability states that the probability of a speciﬁc outcome is the proportion over the long run (if we keep repeating a random process indeﬁnitely) - EX. if the probability is 0.5, no matter how many ﬂips we can expect heads 50% - Probability Notation - P(x): the probability event X occurs - 1- P(x): the probability event X doesn’t occur - EX. Probability of rain tomorrow is 0.3, probability it wont rain is 1- 0.3 = 0.7 - Standardization and Z-Scores - When values are standardized, they are put into some kind of common unit - Z-Score- value that has been standardized in this manner: an observed value of a variable by ﬁnding the distance from its mean in terms of standard deviation -If the mean and standard deviation are unknown…. X to Z to P N (0,1) Normal Distribution - Reference point- center of distribution - EX. ACT and SAT - EX. ACT: Z= 25-21 / 4.7 = 0.851 SAT: Z= 1150-1008 / 114 = 1. 246 -Puts the two test scores in the same unit so they can be accurately compared -Interpretation of Z- Scores -Positive score means the observation is above the mean and vise versa for when the score is negative - Magnitude indicates how far away the data point is from the mean in terms of standard deviation - Z scores put whatever you’re comparing in the same unit - Chebyshev’s Rule -gives the values in the distribution must lie within K standard deviations of the mean -EX. (1- (1/2^2)) X 100 = 75% - Normal Distribution - Bell shape also known as Gaussian - Chebyshev’s rule applies to any distribution - Empirical Rule- like Chebyshev’s Rule, but tailored speciﬁcally to normal distributions - Standard Normal Distribution • Horizontal Axis is Z - The Empirical Rule • Tells us what % of the values fall within 1,2, and 3 standard deviations of the mean • Comparable to Chebyshev’s Rule but only applies to normal distributions