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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 values often specify 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 statistic values. - Results from random samples of size n. Central Limit Theorem: - Random samples from non-normal population 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 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 sample from 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 variable. - 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 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 grand average of sample statistics. - Calculates nk measurements on process variable. 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 sample. - Calculating defective item proportion. CLT Sampling Distribution - Approximately normal distribution. - Most values fall within interval. Process Out of Control: - Values outside 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.