Define the sampling distribution of a statistic

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Define the sampling distribution of a statistic . Define an unbiased statistic and an unbiased estimator . Describe what is meant by the variability of a statistic . Construction Objectives: Students will be able to: Explain how to describe a sampling distribution. Explain how bias and variability are related to estimating with a sample. Vocabulary: Parameter – a number that describes the population Statistic – a number that can be computed from the sample data without making use of any unknown parameters μ (Greek letter mu) – symbol used for the mean of a population x ̄ (x-bar) – symbol used for the mean of the sample Sampling Distribution (of a statistic) – the distribution of values taken by the statistic in all possible samples of the same size from the same population Bias – the level of trustworthiness of a statistic Unbiased Statistic – a statistic whose sampling distribution mean is equal to the true value of the parameter being estimated; also known as an unbiased estimator Variability (of a statistic) – a description of the spread of the statistic’s sampling distribution Key Concepts: Population Parameters Usually unknown and are estimated by sample statistics using techniques we will learn Mean: μ Standard Deviation: σ Proportion: p Sample Statistics Used to estimate population parameters Mean: x ̄ Standard Deviation: s Proportion: p ̂ Sampling Distribution In other words: a sampling distribution of proportions is using the proportion of an individual sample as the data point of the samples of p ̂ – the “bigger” sample. Population of passengers going through the airport Daily sample of 100 Daily sample of 100 Daily sample of 100 Daily sample of 100 Daily sample of 100 Daily sample of 100 Sampling Distribution of p ̂
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Chapter 9: Sampling Distributions Example 1: Upon entry to an airport’s customs area each passenger presses a button and either a green arrow comes on (directing the passenger on through) or a red arrow comes on (directing them to a customs agent) and they have the bags searched. Homeland Security sets the “search” parameter at 30%. a) What type of probability distribution applies here? b) What are the mean and standard deviation of this distribution? c) Each of you represents a day, 8 in total, that we are going to simulate a simple random sampling of 100 passengers passing through the airport. We want to know what your individual average proportion of those who got the green arrow. This we will refer to as p-hat or p. To do this we will use our calculator. ̂ d) We can also use our calculator to simulate this and just get the total number, which represents p-hat or p. ̂ e) Describe the distribution below Example 2: Which of these sampling distributions displays large or small bias and large or small variability?
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