# Quantitative Analysis

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Q: In describing confidence intervals on a mean, z and t intervals are frequently mentioned. How are z and t confidence intervals different? Choose one interval and give an example of how it could be applied within an operations or production environment.
T interval calculates: * The confidence interval for an unknown population mean when the population standard deviation is unknown; * The confidence interval for the difference between two population means when both population standard deviations are known. * T distribution shares characteristics of normal distriution, such as: bell-shape, symmetric about the mean, mean median or mode are equal to 0 and located in center of distribution.
Z interval calculates: * The confidence interval for an unknown population mean when standard deviation is known; * The confidence interval for the difference between population means when the standard deviations of two samples are known; * uses the number of data items to calculate the confidence interval for an unknown proportion of successes; * uses the number of data items to calculate the confidence interval for the difference between the proportion of successes in two populations;

Keep in mind: we are able to use the normal distribution to construct our confidence interval because of the Central Limit Theorem. When n≥30, the sampling distribution of the sample mean becomes normal. If n≤30, the skewness of the population could influence the shape of the sampling distribution and make it not normal.
But what do we do if we want to calculate confidence interval for a sample size where n≤30? We use the t-distribution, but only if we feel it is appropriate to assume that the population distribution itself is normal (or closes to normal).
Constructing confidence intervals with t-distribution is the same as using the z-distribution, except it...

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