1. Math 145
January 28, 2015

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 a representative 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
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.