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Confidence intervals are usually created as part of a statistical test of hypotheses. The hypothesis test is designed to help us make an inference about the true population value at a desired level of confidence. Confidence limits may be determined so that the interval between these limits will cover a population parameter with a certain confidence, that is, a certain proportion of the time. These intervals are called tolerance intervals, and the end points of such intervals are called tolerance limits.

Confidence intervals are the success rate of the research results. In other words, if the confidence level is 95%, then 95 times out of 100 the population percentage, if it could be measured, would be within the confidence interval, and 5 times out of 100 the population percentage would be outside the confidence interval. Problem Statement and Hypothesis Testing Hypothesis testing could be used as a foundation in research projects to determine which path to follow. For example for research you want to determine if converting to a small smart chip oriented keychain fob credit card or continuing with the traditional type of credit card. Researchers are looking for results such as a difference between means by using a test such as ANOVA or even a t-test; a difference between proportions that can be tested using chi-square comparison testing or a relationship either as with a correlation or possibly multiple regressions.

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One way to consider this would be to go to the other technology groups with the concept of putting a credit card smart chip within a keychain size fob. This is like looking for a statistical difference. There are at least four outcomes for that could come from the hypothesis itself. Two are correct and two are wrong. The results may find that this process being so minutely small will not work as simply or one may find that this does work and is not that complex. Independent of this, the technology groups may say this will work easily with a high cost or the technology groups may say this will work easily with minimal costs.

Statistical inference generally involves four main steps. 1. Formulating a hypothesis about the population or “state of nature,” 2. Collecting a sample of observations from the population, 3. Calculating statistics based on the sample, 4. Either accepting or rejecting the hypothesis based on a pre-determined acceptance criterion. There are two types of error associated with statistical inference Type I error ( error) which is the probability that a hypothesis that is actually true will be rejected. The value of (alpha) is known as the significance level of the test. The other type is Type II error ( error) which is the probability that a hypothesis that is actually false will be accepted.

Statistical Concepts To apply some of the concepts acquired within the Statistics for Managerial Decisions course, a survey of those in my department was given regarding usage of the new ExpressPay keychain fob to determine usage. With the quantity of times used the data was gained was calculated following data using the MegaStat program within Excel.