Parameters: Numerical Descriptive Measures - Measures population size. Normal Distribution Overview - Location and shape described by m and s. Binomial Distribution Overview - Cons... 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. Sampling Distributions in Statistics - 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 nonnormal 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. Nearly Normal Distributions in Large Statistics. 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 Nonnormal 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. Mean & Standard Deviation. 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. Read more