AEM 201 1st Edition Lecture 15PREVIOUS LECTUREI. Continuous Probability DistributionsII. Some Important Continuous Probability DistributionsCURRENT LECTUREI. Sampling DistributionII. Methods of Sampling-Probability Sampling TechniquesIII. Nonprobability Sampling TechniquesIV. Point EstimationV. Desirable Characteristics of Point EstimatorsSAMPLING DISTRIBUTIONS- Population: collection of all possible elements of interest- Census: collection of the values for all variables of interest that correspond to all elements of a populationo Number of elements denoted as N- Parameter: a summary measure of used to describe values of a variable for an entire population- Sample: a collection of elements that comprise a subset of the populationo Size of sample denoted as n- Statistical Inference: using data obtained through sampling to estimate the value of or test or test a hypothesis about a parameter (use of inductive logic)o Estimate of parameter- Sampling with Replacement: selection of sample objects where a sample object is not returned to the population after selection and cannot be chosen againMETHOD OF SAMPLING-PROBABILITY SAMPLING TECHNIQUES- Simple Random Sampling: each possible sample of size n chosen from a population of size N has an equal probability of being selected-most common and straight forward of all probability sampling methods- Stratified Random Sampling: a probability sampling method for which we divide the population into homogenous strata and take a simple random sample from each strata (male/female etc.)These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.- Cluster Sampling: a probability sampling method for which we divide the population into heterogeneous clusters (usually by proximity) and take a census from randomly selected clusters- Systematic (Chunk) Sampling: a probability sampling method for which we randomly select the 1st element then subsequently select every kth elementNONPROBABILITY SAMPLING TECHNIQUES- Convenience (Chunk) Sampling: a nonprobability sampling method for which elements are selected on the basis of their ease of collection- Judgment Sampling: a nonprobability sampling method for which elements are selected on the basis of the sampler’s opinion of their appropriatenessPOINT ESTIMATION- Point Estimate: a single numerical value used as an estimate of the parameter- Point Estimator: the sample of statistic that provides the point estimate of the parameter- Precision: the exactness of an estimator- Accuracy: the correctness of an estimator- What is the relationship between precision and accuracy?o Point estimators are: Perfectly precise Almost certainly inaccurateo There is a tradeoff between precision and accuracy. There must be a balance of bothDESIRABLE CHARACTERISTICS OF POINT ESTIMATORS- Unbiasedness: the expected value of the sample (point) estimators (statistic) equals the population value (parameter)- Biased sample estimatorso Sample maximums underestimate the population maximumo Sample minimums overestimate the population minimumo Sample medians could overestimate or underestimate the population mediano Sample ranges underestimates the population range- Unbiased sample estimatorso Sample means are unbiased estimators of the population meano Sample proportions are unbiased estimators of the population proportion- If you collect every sample of the mean and proportion it will equal the