# Decision of Uncertainty

Decision of Uncertainty
QNT/561
January 18, 2010
Louis Daily

Decision of Uncertainty
Confidence intervals can be used to make estimations about population parameters since confidence intervals represent an assortment of possible values for the parameter.   In statistical inference, one wishes to estimate population parameters using observed sample data. This paper will develop this probability concept to formulate a decision. It will explain research methods and processes for limiting the uncertainty in the decision.
Scenario
XYZ Company currently has a 10% defective rate for one of its goods. Upper management is interested in improving the production process to shrink this rate. The proposed solution required an investment of \$400,000 for retraining of production employees and new equipment. Before approving these changes, management wanted to know if the new process will lessen the defective rate. In this scenario, a random sample from the population run of 400 units was observed, 20 failed to meet specification. This information will help answer management’s question.
The question asked by management represents a decision problem in which one has to decide between two possible outcomes. In this scenario, the two possible outcomes are the rate is not lower than 10% and the defective rate is lower than 10%. This process is known as hypothesis testing. Hypothesis testing is the use of statistics to determine the probability that a given hypothesis is true. The usual process of hypothesis testing consists of four steps. These steps are as follows:
1. Identify the null hypothesis H0 and the alternate hypothesis HA. A null hypothesis is a hypothesis set up to be nullified or refuted in order to support an alternative hypothesis, which states there is a difference between the procedures. These hypotheses can be stated in the following terms:
a. H0: μ ≥ .10
b. HA: μ < .10

2. When used, the null hypothesis is presumed true until statistical evidence...