Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 1-1 A Population is the set of all items or individuals of interest Examples: All likely voters in the next election All parts produced today All sales receipts for November A Sample is a subset of the population Examples:1000 voters selected at random for interview A few parts selected for destructive testing Every 100 th receipt selected for audit Populations and Samples

Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 1-2 Sampling Techniques Convenience Sampling Nonprobability/ Nonstatistical Sampling Judgement Probability/Statistical Sampling Simple Random Systematic Stratified Cluster

Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 1-3 Nonprobability Sampling Nonstatistical sampling  samples selected using convenience, jugement, or other nonchance prosesses. Convenience sampling: Samples selected from the population based on accessibility or easy of selection.

Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 1-4 Probability Sampling Items of the sample are chosen based on known or calculable probabilities Statistical/Probability Sampling Simple Random SystematicStratifiedCluster

Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap Simple Random Sampling Every individual or item from the population has an equal chance of being selected. Selection may be with replacement or without replacement. Samples can be obtained from a table of random numbers or computer random number generators.

Example: There are 185 students  you will pick up only 5 students as samples. How do you choose the samples ?  Use the random number. 1. Simple Random Sampling

Random Numbers Table

START 1. Simple Random Sampling

How to use a random number table Let's assume that we have a population of 185 students and each student has been assigned a number from 1 to 185. Suppose we wish to sample 5 students (although we would normally sample more, we will use 5 for this example). Since we have a population of 185 and 185 is a three digit number, we need to use the first three digits of the numbers listed on the chart. We close our eyes and randomly point to a spot on the chart. For this example, we will assume that we selected in the first column. We interpret that number as 206 (first three digits). Since we don't have a member of our population with that number, we go to the next number 899 (89990). Once again we don't have someone with that number, so we continue at the top of the next column. As we work down the column, we find that the first number to match our population is 100 (actually on the chart). Student number 100 would be in our sample. Continuing down the chart, we see that the other four subjects in our sample would be students 049, 082, 153, and Simple Random Sampling

Microsoft Excel has a function to produce random numbers. The function is simply: =RAND() Type that into a cell and it will produce a random number in that cell. Copy the formula throughout a selection of cells and it will produce random numbers between 0 and 1. If you would like to modify the formula, you can obtain whatever range you wish. For example, if you wanted random numbers from 1 to 250, you could enter the following formula: =INT(250*RAND())+1 The INT eliminates the digits after the decimal, the 250* creates the range to be covered, and the +1 sets the lowest number in the range. 1. Simple Random Sampling

Example: If you want to select 10 sample students from 100 students, you could type in a cell the following formula: =INT(100*RAND())+1 After that, a number (between 1 – 100) will appear then copy that formula to other 9 cells (below, up, right or left from the first cell). You can find the ten numbers (between 1 – 100) which selected randomly as samples: Number of students which chosen randomly as sample 1. Simple Random Sampling

Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap Stratified Sampling Population divided into subgroups (called strata) according to some common characteristic Simple random sample selected from each subgroup Samples from subgroups are combined into one Population Divided into 4 strata Sample

Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 1-13 Decide on sample size: n Divide frame of N individuals into groups of k individuals: k=N/n Randomly select one individual from the 1 st group Select every k th individual thereafter 3. Systematic Sampling N = 64 n = 8 k = 8 First Group

Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap Cluster Sampling Population is divided into several “clusters,” each representative of the population A simple random sample of clusters is selected All items in the selected clusters can be used, or items can be chosen from a cluster using another probability sampling technique Population divided into 16 clusters. Randomly selected clusters for sample

What Size Sample Is Needed? Some principles : 1.The greater the dispersion or variance, the larger the sample. 2.The greater precision of the estimate, the larger the sample. 3.The narrower or smaller the error range, the larger the sample. 4.The higher the confidence level, the larger the sample. 5.The greater the number of subgroups of interest within sample, the larger the sample. 6.The lower cost/respondent, the larger the sample.

Determining Sample Size Formula: where: n = sample size Z α/2 = 1.96 (from table of Z distribution, α = 0.05) E = Margin Error (known) σ = Standard deviation (known) Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 1-16

Determining Sample Size Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 1-17