B.            Probability and statistics

                                                       1.            Drawing valid statistical conclusions
Distinguish between enumerative (descriptive) and analytical (inferential) studies, and distinguish between a population parameter and a sample statistic. (Apply)

                                                       2.            Central limit theorem and sampling distribution of the mean
Define the central limit theorem and describe its significance in the application of inferential statistics for confidence intervals, control charts, etc. (Apply)

                                                       3.            Basic probability concepts
Describe and apply concepts such as independence, mutually exclusive, multiplication rules, etc. (Apply)

Enumerative (descriptive) studies – data that can be counted. Calculated from a sample are numerical, descriptive measures called statistics. When the measures describe a population, they are called parameters.

Analytical (inferential) studies – draw conclusions about a population characteristics based upon sample information.

Central limit theorem - The central limit theorem states that given a distribution with a mean m and variance s2, the sampling distribution of the mean approaches a normal distribution with a mean and variance/N as N, the sample size increases. The significance of the central limit theorem on control charts is that the distribution of sample means approaches a normal distribution. For most distributions, a near normal sampling distribution is attained with a sample size of 4 or 5.

Basic probability – most quality theories use statistics to make inferences about a population based on information contained in samples. The mechanism used to make inferences is probability. Probability refers to the chance of something happening, or the fraction of occurrences over a large number of trials. Probability can range form 0 (no chance) to 1 (certainty).