Statistical Inference and Sampling Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Simple Random Sampling All items in the population have the same probability of being selected. Finite Population: To be sure that a simple random sample is obtained from a finite population the items should be numbered from 1 to N. Nearly all statistical procedures require that a random sample is obtained. Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Estimation The population consists of every item of interest. The sample is randomly drawn from the population. Sample values should be selected randomly, one at a time, from the population. Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Random Sampling and Estimation Figure 7.1 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Distribution of X The mean of the probability distribution for X = Standard error of X = standard deviation of the probability distribution for X =  x Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Distribution of X Figure 7.6 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Distribution of X Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Probabilities in the Sampling Distribution of X Figure 7.8 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Central Limit Theorem When obtaining large samples from any population, the sample mean X will follow an approximate normal distribution. What this means is that if you randomly sample a large population the X distribution will be approximately normal with a mean  and a standard deviation (standard error) of  x   n Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Central Limit Theorem Figure 7.10 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Central Limit Theorem Figure 7.11 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Central Limit Theorem Figure 7.12 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Confidence for the Mean of a Normal Population (  known) Figure 7.16 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Confidence for the Mean of a Normal Population (  known) P(-1.96  Z  1.96) Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Confidence for the Mean of a Normal Population (  known) (1-  ) 100% Confidence Interval Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Confidence for the Mean of a Normal Population (  unknown) Student’s t Distribution Population variance unknown Degrees of freedom = n - 1 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Student’s t Distribution Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Confidence for the Mean of a Normal Population (  unknown) X –  s / n t = Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Selecting Necessary Sample Size Known  Sample size based on the level of accuracy required for the application. Maximum error: E –Used to determine the necessary sample size to provide the specified level of accuracy –Specified in advance –Equation: Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Selecting Necessary Sample Size Known  E  Z  /2  n       Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Selecting Necessary Sample Size Unk nown  n  Z  /2  s E       2 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Other Sampling Procedures Population: the collection of all items about which we are interested. Sampling Unit: a collection of elements selected from the population. Cluster: a sampling unit that is a group of elements from the population, such as all adults in a particular city block. Sampling frame: a list of population elements Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Other Sampling Procedures Strata: are nonoverlapping subpopulations. Sampling design: specifies the manner in which the sampling units are to be selected. Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Systematic Sampling The sampling frame consists of N records. The sample of n is obtained by sampling every kth record, where k is an integer approximately equal N/n. The sampling frame should be ordered randomly. Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Stratified Sampling Stratified sampling obtains more information due to the homogenous nature of each strata. Stratified sampling obtains a cross section fo the entire population. Obtain a mean within each strata as well as an estimate of . Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Cluster Sampling Single-stage cluster sampling: randomly select a set of clusters for sampling. Include all elements in the cluster in your sample. Two-stage cluster sampling: randomly select a set of clusters for sampling. Randomly select elements from each sampled cluster Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing