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STA309 - Exam II cheat sheet

STA309 - Exam II cheat sheet - STA309 Exam II Probability...

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STA309 Exam II Probability and Sampling Random phenomenon: if individual outcomes are uncertain but there is nonetheless a regular distribution of outcomes in a large number of repetitions Parameters and Statistics: o Parameter: describes the population; usually unknown. written as Greek letters (like µ and σ ). o Statistic: describes a sample; computed from the sample data; written w/ letters (like J and s ). J is a random variable (numerical outcome of a random phenomenon). J is rarely exactly right. use statistics to est. parameters. Use J, to est. pop, µ . Sampling Variability: value of a statistic (like J) will be different for different samples. Randomness: individual result can’t be predicted (short run); pattern/regular distribution emerges after repetitions (long run). o ** To reduce bias, use random sampling. To reduce variability, use a larger sample.** o Probability: probability of any outcome of a random phenomenon is the propor. of times the outcome occurs in a very long series of repetitions. o Independence: the outcome of one trial does not influence the outcome of any other. To explore randomness, you need a long sequence of independent trials Law of large numbers: As the number of observations increases, the mean J of the observed values gets closer to the mean µ. It is reasonable to use J to estimate µ. The larger the sample, J will come to the “truer” mean of the population. Sample means: o Suppose J is the mean of an SRS of size n from a large population. J is a random variable & unbiased estimator. o The distribution of J is called a sampling distribution ; sampling distribution has mean µ and sd = σ /√n. o Averages are less variable than individual observations. o The results of large samples are less variable than the results of small samples. o If a pop. has the N(µ, σ ) distribution, then sample mean J of n observations has the Normal dist: N(µ, σ /√n) ** Central Limit Theorem: For any population with mean µ and finite standard deviation σ , when n is large the sampling distribution of the sample mean, J, is approximately normal. o If the histogram is skewed, you probably did something wrong. In the central limit theorem, even if the population is not normal, the sample population mean will look normal if n is very large Statistical Control Statistical Control: Process results will vary in spite of efforts to be consistent. Ex: weight, dimensions of manufactured items. Processes can be “controlled” to be within acceptable limits. A variable is said to be in statistical control (or in control) when it continues to be described by the same distribution when observed over time. Statistical process control o Purpose: to monitor a process so that any changes can be detected and quickly corrected.
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