# TAMU STAT 211 - STAT-211 CHeat Sheet Exam 2 (2 pages)

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**View the full content.**## STAT-211 CHeat Sheet Exam 2

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## STAT-211 CHeat Sheet Exam 2

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- School:
- Texas A&M University
- Course:
- Stat 211 - Prin Of Statistics I

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Definitions Alternative Hypothesis Ha is either 0 0 or Equations Binomial 0 Categorical variable Places a unit into one of several categories male female succeed fail republican democrat approve disapprove not sure Census A sample that attempts to include the entire population all units Complement AC all elements not in the set conditional probabilities P A B if B happens the probability that A happens P A B P A B P B H0 is n x n x p 1 p n x x 0 Observational study Measure quantities of interest for a particular group This is passive data collection in that on does not attempt to influence the group Outliers Unusually small or large values Parameter A fixed usually unknown number that describes the population percentile the value such that p of values are below it and 100 p are above it Population The entire set of units Probability a number between 0 and 1 inclusive indicating the likelihood that the event will occur p value the probability of obtaining a Z more consistent with the alternative hypothesis than z The p value quantifies the strength of evidence in favor of the alternative hypothesis The smaller the p value the stronger the evidence for the alternative hypothesis We reject the null hypothesis if and only if the p value is less than the for the test Quantitative variable Takes on numerical values for which arithmetic makes sense SAT score number of siblings cost of textbooks Random process a process whose outcome cannot be predicted with certainty random variable a function mapping each element of the sample space to the real numbers randomized subjects are randomly assigned to control or treatment group ensures that the only difference between the two groups is what they are injected with Relative frequency proportion of the data with the value e x Probability x x actual successes in region average number of successes in region Variance Mean of Distribution Expected Value Uniform 1 k Probability k number of outcomes Normal Curve PDF x 1 x n i 0 i 2 Z score sample variance s is the sum of squared deviations from the sample mean divided by n 1 Z Sample A set of selected units and associated measurements Sampling Distribution of the Mean The distribution of x s 2 i 1 n 1 dx x 2 1 B Mean Variance Bernoulli Mean p probability Variance 2 p 1 p Standard deviation sqrt variance Confidence Intervals For n 30 With known CI When is unknown s x t 2 n n x z n 1 2 n x i x 2 i 1 n 1 sn For proportions b Gamma CI x i x 2 mean standard deviation a For n 30 n x 2 2 P a X b PDF Probability Sample median is the middle observation if the values are arranged in increasing order Sample space S the collection of all possible outcomes to a random process sample standard deviation s is the square root of the variance 2 1 e 2 n Sample mean of n observations is the average the sum of the values divided by n x successes n trials p probability of success of each trial Mean n p Expected Value n p Variance n p 1 p Poisson continuous random variable random variable that takes a uncountably infinite number of values 1 Uniform A B all values between A and B are equally likely 2 Normal 2 mean is and variance is 2 bell shaped pdf 3 Gamma used for time until event when the occurrence of events follows Poisson process Control Group A collection of experimental units subjected to the same conditions as those in an experimental group except that no treatment is imposed discrete random variable random variable that takes a finite or countably infinite set of value 1 Bernoulli p either 0 or 1 p is probability of 1 2 Binomial n p number of success in n trials n for number of trials and p for probability of success on each trial 3 Poisson often used for number of occurrences in time or space interval is mean number of occurrences in interval double blinded neither the subjects receiving the treatment nor the individuals recording the responses know who is in the control group and who is in the treatment group Event A B a collection of possible outcomes Simple one outcome Compound more than one outcome Experiment Deliberately impose treatments on groups in order to observe responses The purpose is to study whether the treatments cause a change in the responses Experimental Group A collection of experimental units subjected to a treatment Frequency number of times the value occurs in the data If A and B are independent then AC and BC are independent If A and B are independent then P A B P A So A and B independent translates to B happening does not change the probability that A happens Independence A B are independent if P A B P A P B Interquartile range IQR Q3 Q1 the range of the middle 50 of the data Intersection A B all elements in A and B level of significance determines the amount of evidence we require in order to reject the null The value of specifies the probability of rejecting the null if it is true type 1 error is typically set less than 0 1 If p value then we reject H0 If p value then we fail to reject H0 Mode A significant peak in the histogram Multimodal data has more than one significant mode bimodal 2 modes Multivariate data two or more variables measured for each unit Mutually exclusive two events are mutually exclusive if they have no outcomes in common Null Hypothesis Probability p 1 x i n i 1 p 1 p Var p n CI x z 2 s n use t table when n 30 or has unknown population standard deviation

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