0000019367 00000 n tB d��BC�����KX�1F�BF�qy�a��`:�C�)l�`{?�'$� 0000002453 00000 n The central limit theorem (CLT) tells us no matter what the original parent distribution, sampling distribution of X¯ is typically normal when n ≥ 30. An event is a subset of the sample space. 0000012872 00000 n trailer This is called the Central Limit Theorem and is the backbone of most of the statistical analysis we will perform in the future. 0 What happens as n increases? (a) 5 :750 (b) 5 :752 0 (c) 5 :753 0 120 Part 2 / Basic Tools of Research: Sampling, Measurement, Distributions, and Descriptive Statistics There are three different types of distributions that we will use in our basic task of observation and statistical generalization. 0000043204 00000 n 11 X This is the histogram that results from 100 different samples, each with 32 students. 0000002122 00000 n Sampling Distribution of Means and the Central Limit Theorem 39 8.3 Sampling Distributions Sampling Distribution In general, the sampling distribution of a given statistic is the distribution of the values taken by the statistic in all possible samples of the same size form the same population. %PDF-1.5 %���� Probability and Statistics Notes Pdf – PS Pdf Notes book starts with the topics Binomial and poison distributions & Normal distribution related properties. We will see that the means of the samples are normally distributed, regardless of the distribution of the original population. 0000041887 00000 n The sampling distribution arises due to the sample, and therefore the statistic values generated from the sample data themselves, being a random outcome. Sampling distributions are probability distributions of statistics. A lot of data drawn and used by academicians, statisticians, researchers, marketers, analysts, etc. 0000042908 00000 n Page 5.2 (C:\Users\B. • The normal distribution is easy to work with mathematically. The mean of the sampling distribution is 5.75, and the standard devia-tion of the sampling distribution (also called the standard error) is 0.75. 0000034994 00000 n Many people have written excellent notes for introductory courses in probability. The sampling distribution of a statistic (in this case, of a mean) is the distribution obtained by computing the statistic for all possible samples of a specific size drawn from the same population. Simulating a Sample Distribution for a Sample Mean Three things that we should notice (See notes slide 3): 1.The population was bell shaped and the sampling distributions were also bell shaped 2.As the sample size was increased from 10 to 100, the variability in the graph became smaller. Probability sampling (a term due to Deming, [Deming]) is a sampling porcess that utilizes some form of random selection. NOTES: Sampling Distributions n = sample size x = sample mean = average of a quantitative variable describing a SAMPLE µ ... Sampling Distribution : The sampling distribution of a statistic is the distribution of values taken by the statistic in all possible samples of the same size from the same population. I only Il only 111 only 11 and 111 only l, 11, and 111 Which of the following is NOT true concerning sampling distributions? studying. • The Laurier company’s brand has a market share of 30%. Binomial distribution for p = 0.5 and n = 10. About these notes. It is helpful to sketch graphs of each! 0000018869 00000 n 2 7 Example: Sampling Distribution for a Sample Proportion • Suppose (unknown to us) 40% of a population carry the gene for a disease (p = 0.40). which are; Quota sampling, Accidental sampling, %%EOF STA408: Statistics for Science and Engineering Chapter 2: Estimation 2.1 Sampling This concept is Sampling distributions are vital in statistics because they offer a major simplification en-route to statistical implication. 0000036464 00000 n 0000019325 00000 n 0000043805 00000 n I.4 Sampling Lecture Notes 1. We can graph the PDF and CDF (images from Wikipedia) using various values of the two parameters: The normal distribution is sometimes colloquially known as the "bell curve" because of a it's symmetric hump. What is the probability that more than 32% of the respondents say they prefer the Laurier brand? 0000012254 00000 n [Note: There is a distinction • Although we expect to find 40% (10 people) with the gene on average, we know the number will vary for different samples of n = 25. h��Ymo�6�+�ؠp��"�"@�4��&1jo)`��b��6�2dK���H�֛_����ɻ�s���Dk…"�R� 5#�a�I�� �j�(ɡc � Binomial distribution for p = 0.08 and n = 100. Goals of a good sample from the correct population chosen in an unbiased way large enough to re ect total population 14. Specifically, it is the sampling distribution of the mean for a sample size of 2 (N = 2). STAT-3611 Lecture Notes 2015 Fall X. Li. 0000046171 00000 n I wish to acknowledge especially Geo rey Grimmett, Frank Kelly and Doug Kennedy. Letusdescribethe sample space S, i.e. 0000041336 00000 n Sampling distributions Distribution – sampling distributions of means,Sample space and events Probability The axioms of probability h�bbd``b`�$�� �� �2,�0�H�;�z �+�8$�[@�D �v �����-��4*@,Y �������H����0 O| 62 Part 2 / Basic Tools of Research: Sampling, Measurement, Distributions, and Descriptive Statistics Chapter 6 Sampling A s we saw in the previous chapter, statistical generalization requires a representative sample. Section 8.4. 0000038992 00000 n as ngets larger. endstream endobj 74 0 obj <> endobj 75 0 obj <> endobj 76 0 obj <>stream The Sampling Distribution of x We are able to show 2 Ex( ) and Var(x) n σ ==µ . %%EOF Normal Approximation to the Binomial Basics Histograms of number of successes Hollow histograms of samples from the binomial model where p = 0:10 and n = 10, 30, 100, and 300. 117 0 obj <>stream 0000035820 00000 n 0000044439 00000 n NOTE: If the original ‘parent population’ from which the sample was drawn is normal, then X follows a normal distribution for any n(a linear combination of normals is normal), and the CLT is not needed to achieve normality. 0 These are the population distribution, which represents the distribu- [Raj, p4] The surveyor’s (a person or a establishment in charge of collecting and recording data) or researchers initial task is to formulate a rational justification for the use of sampling in his research. /]���s�{��ċ x��HC��-����SN�w[�gڻ�E�+�^^�/# Being ‘reasonably certain’ is enough!” Pavel E. 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