## Sample Size on Confidence Intervals and Hypothesis Testing for Inferences Making #### Sample size for confidence intervals for the difference between two means (mainstream) To determine the sample size for a confidence interval for the difference of two means to have a specified margin-of-error we need to apply the following formula: #### Sample size for confidence intervals on the proportion using classical theory (mainstream) Knowing the proportions of some occurrence over all possible occurrences is important in countless applications. A politician would like to know what proportion of voters in his electorate will vote for him. #### Sample size for confidence intervals on the standard deviation The biggest enemy for quality and cost is variability. For example, in manufacturing the greater the variability, the greater the chance of producing non-conforming product. #### Sample size for confidence intervals on the mean To determine the sample size for a confidence interval to have a specified margin-of-error we need to apply the following formula: N = Z_Value(alpha / 2) * Sigma / (margin-of-error)^2. Where alpha is the specified level of significance. #### Sample size for confidence intervals for the Cp and Cpk index The Cp and Cpk Index has been used for many decades in Quality Assurance as a means of summarizing process capability into a simple index. #### Sample size for hypothesis testing on the standard deviation It can be argued that philosophically the standard deviation is more important than the mean. The standard deviation is a measure of variability and some have called variability Quality’s biggest enemy. #### Sample size for hypothesis testing for the ratio of two standard deviations The theory behind hypothesis testing for the ratio of two standard deviations is based on the theory for hypothesis testing of two variances where the variance is equal to the standard deviation ^2. #### Sample size for hypothesis testing for the proportion Hypothesis testing for the proportion has one of the most diverse applications and is relevant particularly in manufacturing, health, political campaigning and market research. #### Sample size for hypothesis testing for the Cp and Cpk index The Cp and Cpk index remain one of the most popular Quality Indexes used by manufacturing. The baseline is considered 1.0 being the borderline case. #### Sample size for hypothesis testing on the mean There are many situations where it is necessary to obtain an average reading of some variable. For example, the average calorie consumption by people from various demographic categories per day. #### Sample size for hypothesis testing on the difference between two means There are many situations where the analyst needs to decide on the difference between two means. Several researchers have reported that the difference in two means can be more important than information on the means separately. www.qtechinternational.com