Hypothesis Testing - Paper

Topics: Statistics, Statistical hypothesis testing, Statistical tests Pages: 14 (4252 words) Published: February 14, 2013
Hypothesis Testing

* 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...
Continue Reading

Please join StudyMode to read the full document

You May Also Find These Documents Helpful

  • Statistical Hypothesis Testing and Linear Regression Essay
  • Essay about hypothesys testing
  • One Sample Hypothesis Testing Paper
  • Essay on Hypothesis Testing
  • Essay on Statistical Hypothesis Testing and Pic
  • One Sample Hypothesis Testing Essay
  • What is Hypothesis Testing Essay
  • Past Exam Paper

Become a StudyMode Member

Sign Up - It's Free