Statistical Inference Statistics PDF
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This document covers statistical inference statistics, numerical descriptive measures, normal distribution, binomial distribution, and parameters in distributions. It also includes information about sample reliance on parameters, sample variability, repeated sampling, sampling distribution of statistics, and the central limit theorem.
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Parameters: Numerical Descriptive Measures Measures population size. Normal Distribution Overview Location and shape described by m and s. Binomial Distribution Overview Consists of n trials. Location and shape determined by p. Parameters in Distribution Unknown value...
Parameters: Numerical Descriptive Measures Measures population size. Normal Distribution Overview Location and shape described by m and s. Binomial Distribution Overview Consists of n trials. Location and shape determined by p. Parameters in Distribution Unknown values often specify the distribution form. Sample Reliance on Parameters Essential for understanding parameters. "Statistics Overview" Calculated numerical descriptive measures. Descriptive measures from samples. "Sample Variability in Statistics" Variations across samples. Random variables. Repeated Sampling Overview Indicates possible values and frequency of each value. Sampling Distribution of Statistics Defines probability distribution of possible statistical values. Results from random samples of size n. Central Limit Theorem: Random samples from non-normal populations with finite mean and standard deviation. Large ns lead to approximately normal distribution of sample mean. Approximation becomes more accurate with larger ns. Central Limit Theorem: Assumes the sum of n measurements is normal. Involves mean nm, standard deviation. Statistical Inference Statistics Sums or averages of sample measurements. "Understanding Behavior and Inference Reliability" Describe behavior. Evaluate inference reliability. Normal Sample Distribution Ensures normal sampling distribution regardless of sample size. "Sample Population Distribution" Approximately symmetric sample population. Distribution becomes normal for small n values. Skewed Sample Population Requirement Sample size must be at least 30. Distribution should reach approximately normal. Random Sample Selection Selects n-size samples from the population with mean m, standard deviation s. Sample Sampling Distribution Mean: m Standard deviation: -1 Normal Population Distribution Normal sampling distribution for all sample sizes. "Sampling Distribution Normality in Non-normal Populations" Normal distribution observed when n is large. Standard Deviation of x-Bar Also known as Standard Error (SE). Standardizing Interval of Interest If sampling distribution is normal or similar. Rescale interval of interest. "Selecting Random Sample from Binomial Population" Size n Parameter p Sample Distribution Overview Distribution of sample proportion. "Sampling Distribution Overview" Large n. P not close to zero or one. Approximately normal distribution. Standard Deviation of P-hat Also known as Standard Error (SE). Standardizing or Rescaling Interval of Interest If sampling distribution is normal or similar. Rescale interval of interest. Assignable Variable Change Cause Cause can be identified and corrected. "Random Variation Overview" Uncontrolled variation. Process Control Overview Random variation in process variables. Process is in control. Controlling Process Variance Reducing variation. Keeping process variable measurements within specified limits. Production Process: Taking n-samples. Calculating sample mean. CLT Sampling Distribution Approximately normal distribution. Most values fall within interval. Process Out of Control: Values outside the specified interval. Control Chart Creation Collect data on k samples of size n. Use sample data to estimate m and s. Mean Estimation in Process Variables Utilizes the grand average of sample statistics. Calculates nk measurements on process variables. Standard Deviation Estimation Estimated by s, the standard deviation of nk measurements. Control Chart Creation Utilize centerline and control limits. Production Sample Calculation Taking n-size samples. Calculating defective item proportion. CLT Sampling Distribution Approximately normal distribution. Most values fall within interval. Process Out of Control: Values outside the specified interval. Control Chart Creation Collect data on k samples of size n. Estimate p for each sample using sample data. Population Proportion Defective Estimation Estimated with Grand Average of Sample Proportions Calculated for k samples. Control Chart Creation Utilize centerline and control limits.
