Business Statistics: Chapter 8; Sampling Methods and Central Limit Theorem

Sampling Methods

    4 Sampling Methods: used because contacting entire population would be time consuming, cost of studying all items would be too high, physical impossibility of checking all items, and destructive nature of tests.

        1.) Simple Random Sampling: a sample selected so that each item in population has equal chance of being included.

        2.) Systemic Random Sampling: Random starting point selected, then every kth member of population is selected.

        3.) Stratified Random Sampling: population is divided into subgroups, called strata, then a sample is randomly selected from each stratum.

        4.) Cluster Sampling: population divided into clusters, using naturally occurring boundaries like geography, then clusters are randomly selected and a sample is collected from randomly selecting from that cluster.

Sample Mean as Random Variable

    Sampling Error: Difference between a sample statistic and its corresponding population parameter.

        = sample mean - population mean

    or, = population standard deviation / square root of sample size

Sampling Distribution of Sample Mean

    Sampling Distribution of Sample Mean: probability distribution of all possible sample means of a given sample size. Is normally distributed.

        = Sum of all sample means / Total number of samples

        Where total number of samples is found by = N! / n! (N-n)! and N= total number of items in population and n= items in sample

Central Limit Theorem

    Central Limit Theorem: If all samples of a certain size are selected from any population, the sampling distribution of the sample mean is ~a normal distribution. Approximation improves with larger samples.

Standard Error of the Mean

    Standard Error of the Mean= standard deviation in the population / square root of number of observations in each sample.

Using Sampling Distribution of Sample Mean

    Finding Z-Value when population standard deviation is known:

        z = sample mean - population mean / standard deviation/ square root of number of observations

    Sampling Distribution of the Sample Proportion:

        Sample proportion= number of successful outcomes /                                  sample size or total number of outcomes

        Standard Error of the Proportion= Square root of population proportion (1 - population proportion) / total number of outcomes

        Z-Value for Sample Proportion= sample proportion - population proportion / Standard Error of Proportion