STATS 250 1st Edition Lecture 6 Outline of Last Lecture I. What is a Random Variable?II. General Discrete Random VariablesIII. Expectations for Random VariablesIV. Binomial Random VariablesV. General Continuous Random VariablesVI. Normal Random VariablesOutline of Current Lecture I. Parameters, Statistics, and Statistical InferenceII. From Curiosity to Questions about ParametersIII. SD Module 0: an Overview of Sampling DistributionsIV. SD Module 1: Sampling Distributions for One Sample ProportionCurrent LectureI. Parameters, Statistics, and Statistical Inferencea. Because knowing the true population parameter value is nearly impossible, we use a sample value to make an inference about the populationi. To make the inference the most accurate, we use a random sampleb. Statistical Inference: the use of sample data to make judgments or decisions about populationsi. Confidence Interval Estimation1. Confidence interval: range of values that the researcher is fairly confident will cover the true, unknown population parameter value2. Hypothesis testing: uses sample data to attempt to reject a hypothesis about the population.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.a. Specifies a null value for the parameter, and assesses how unlikely the sample statistic would be if the null parameter value were correctII. From Curiosity to Questions about Parametersa. Proportions: used for categorical datab. Means: used for quantitative datac. Most commonly used is the five parameter method: median, first and third quartile, max and minIII. SD Module 0: an Overview of Sampling Distributionsa. Sampling distribution of the statistic: distribution of all possible values of a statistic for repeated samples of the same size from a populationb. Comes from random samplingIV. SD Module 1: Sampling Distributions for One Sample Proportiona. Many samples produce counts, rather than measurements (male/female, republican/democrat, etc.)b. Sample proportion is found by taking the number of “successes” in the sample, and dividing it by the sample sizei. Results in a binomial distributionc. If n is small, binomial distribution is used to find sample proportiond. If n is large, the Normal Curve Approximation Rule for Sample Proportions is usedi. P is the population proportion of interest or binomial probability of successii. p is the corresponding sample proportion or proportion of successesiii. Mean = Piv. Standard Deviation = square root of