Math 145

1. Math 145 September 3, 2014

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.