* Used to prove which are the factors that are actually impacting the mean or standard deviation of the project y. * To see the impact of improvements after they are implemented * P- value is critical in making decisions.

* To determine if the statistical hypothesis is true or false, the entire population should be examined, which becomes impossible for large sizes, Random sampling is done. * The conclusion for the population is based upon statistical significance determined from sample data.

What is a Hypothesis?

* Is used to describe the assumption.

* Is based on the population parameters.

* Must be clearly stated for correct decision-making.

* Is proved based on that evidence from Statistical test. Null Hypothesis. Ho is a statement (assumption) about population(s) parameters. * It is the one assumed to be true unless stated otherwise * Generally describes the present status

Alternate Hypothesis, Ha, is the negation or compliment of the null hypothesis. * Generally describes a difference

Hypothesis Testing

* Let us illustrate the concept using a justice system.

* H0: Person is not guilty

* H1: Person is guilty

* Strong evidence is required to prove a person guilty, that is, to reject the Ho. Hypothesis Testing: Types of error

* Type I error α : Accepting Ha when Ho is the truth. It is also called the level of significance. Generally it is a standard to limit the chance of making a Type I error by setting α= .05. That is, the confidence (-1-, called the confidence level) of accepting Ho when Ho is the true would be 95%. * Type II error β : Accepting Ho when Ha is the truth. We will typically set β= 0.1. The chance of making a Type II error, β, depends on α and sample properties (sample size, centering, standard deviation). The power of test, (=1- β) of detecting the difference (correctly reject Ho) would be 90%. * We assume α - .05 and β=.10. Interpreting it for the legal system, we would tolerate a higher risk of setting free a guilty person (Type II error) than jailing and innocent person (Type I error).

Hypothesis Testing: Acceptance Criteria

* Decision- making for a hypothesis test is done using the p-value. * P-value is the probability of getting the observed difference or greater between your sample means when Ho is true. * If the p-value is less than or equal to a predetermined level of significance (α-level), then the null hypothesis is rejected and the alternative hypothesis is claimed. If p is low, Null must go!

* If the p-value is greater than the α-level, the null hypothesis is accepted and the alternative hypothesis cannot be claimed. * Generally the acceptance level of a Type I error id 0.05. * Thus, any p-value less than 0.05 means we reject the null hypothesis Hypothesis Testing: Choosing α Level

* Choice for α determines the probability of type I error. * If α is small,

* There is less chance of incorrectly rejecting the null hypothesis (Ho). * Power is low, and thus a decreased chance of detecting an effect if one exists. * If α is large,

* There is high chance of incorrectly rejecting H0.

* Power is high, there is high chance of detecting the effect. * Generally α – 0.05, that is the chance of finding an effect that does not really exist is only 5%. In most situations, this is acceptable. * To select α for a particular test, think which mistake would be worse, finding an effect that does not really exist, or not finding an effect that really does exist.

* Choosing α Level Example

* Deciding on the purchase of a new costlier Soldering machine. * Ho: New Soldering machine is same as the old machine * Ha: New Soldering machine is more accurate than the old machine (less defectives) * To be very sure that the new Soldering machine will save money in terms of producing high quality, it is preferable to select...