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Introduction to Statistics: Descriptive and Inferential Analysis

Learn the fundamental concepts of statistics, including descriptive and inferential analysis. Discover various sampling designs, such as simple random sampling, systematic random sampling, cluster sampling, and stratified random sampling with proportional allocation.

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Introduction to Statistics: Descriptive and Inferential Analysis

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  1. Math 145

  2. Statistics is the science of collecting, analyzing, interpreting, and presenting data. Two kinds of Statistics: • Descriptive Statistics. • Inferential Statistics. A statistical inference is an estimate, prediction, or some other generalization about a population based on information contained in the sample.  Use arepresentative sample.

  3. Sampling Designs • Simple Random Sampling. • Systematic Random Sampling. • Cluster Sampling. • Stratified Random Sampling with Proportional Allocation.

  4. Simple Random Sampling • A sampling procedure for which each possible sample of a given size has the same chance of being selected. • Population of 5 objects: {A, B, C, D, E} • Take a sample of size 2. • Possible samples: {(A,B), (A,C), (A,D), (A,E), (B,C), (B,D), (B,E), (C,D), (C,E), (D,E)} • Random number generators

  5. Systematic Random Sampling • Step 1. Divide the population size by the sample size and round the result down to the nearest number, m. • Step 2. Use a random-number generator to obtain a number k, between 1 and m. • Step 3. Select for the sample those numbers of the population that are numbered k, k+m, k+2m, … • Expected number of customers = 1000 • Sample size of 30  m = 1000/30 = 33.33  33 • Suppose k = 5. Then select {5, 5+33, 5+66, …}

  6. Cluster Sampling • Step 1. Divide the population into groups (clusters). • Step 2. Obtain a simple random sample of clusters. • Step 3. Use all the members of the clusters in step 2 as the sample.

  7. Stratified Random Sampling with Proportional Allocation • Step 1. Divide the population into subpopulations (strata). • Step 2. From each stratum, obtain a simple random sample of size proportional to the size of the stratum. • Step 3. Use all the members obtained in Step 2 as the sample. • Population of 10,000 with 60% females and 40% males • Sample of size 80.  48 females (from 6,000) and 32 males (from 4,000).

  8. Homework • Answer # 1, 2, 5, 7, 10. on page 18.

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