Individual : Discussion Questions - Assignment Example

Null Hypothesis Null hypothesis pertains to the hypotheses that were created assuming the likelihood that it will be rejected. The rejection of null hypothesis leads to the acceptance of an alternative hypothesis (Walpole, 1982). One limitation with the null hypothesis is that the data may only reject of fail to reject a null hypothesis, but could not prove it. 2. Hypotheses in Business and Operations Management Hypothesis testing seems to be perceived as a theory in a modern setup. It should, however, be promoted in quality management.

According to Li Zongming, both parametric test (t-test and z-test) and nonparametric test (sign test and Wilcoxon rank-sum test) are appropriate for use in a manufacturing environment. It is however, important, for people within the company to interpret the data and not just focus on the figures returned like the mean and range. Hypothesis testing aids a business to better understand the data and from there, help on production control. For example, operations lead may be required to check if they may still continue to use the machine in the factory.

The mean production quantity of processing machine during operations is supposed to be 300 units.  The factory did a test on one particular engine at randomly selected times.  The mean production quantity of all tests was 285 units. The result of the test will be the basis of the factory on whether they need to have the machine repaired or whether they may continue operations using it. 3. Confidence Interval and Hypothesis Testing Hypothesis testing is a method in analyzing data in order to determine whether a certain result is significant or not.

Confidence interval, on the other hand, is range of population value which is most likely to contain the parameter of interest. As described in Wikipedia (“Confidence Interval”, n.d.): Confidence intervals are closely related to statistical significance testing. For example, if for some estimated parameter ? one wants to test the null hypothesis that ? = 0 against the alternative that ? ? 0, then this test can be performed by determining whether the confidence interval for ? contains 0. More generally, given the availability of a hypothesis testing procedure that can test the null hypothesis ? = ?0 against the alternative that ? ? ?

0 for any value of ?0, then a confidence interval with confidence level ? = 1 ? ? can be defined as containing any number ?0 for which the corresponding null hypothesis is not rejected at significance level ?. In consequence, if the estimates of two parameters have confidence intervals at a given ? value that do not overlap, then the difference between the two values is significant at the corresponding value of ?. However, this test is too conservative. If two confidence intervals overlap, the difference between the two means still may be significantly different 4.

Dependent and Independent Samples Dependent samples are samples which are paired meaning each individual observation of one sample has a unique corresponding member in the other sample whereas, an independent sample is a sample which is an independent entity meaning they are separate samples. An example will be a test made for a group of students. A dependent sample is one wherein the same students taking up the same course, keep taking the same sample from. The same place & do not expand their area of research.

An independent sample is one taken, without the course or school in question being involved. 5. One or Two-hypothesis Test A one-tailed hypothesis test is a test of a statistical hypothesis where the region of rejection is on only one side of the random variable. For example, if the null hypothesis says that the mean is less than or equal to 5. The alternative hypothesis is that the mean is greater than 5. The region of rejection would consist of a range of numbers located on the right side of random variable; which is a set of numbers greater than 5.

A two-tailed hypothesis on the other hand, is a test of a statistical hypothesis wherein the region of rejection is on both sides of the random variable. For example, if the null hypothesis says that the mean is equal to 5. The alternative hypothesis is that the mean is less than or greater than 5. The rejection would consist of a range of numbers located on both sides of random variable; that is, the region of rejection would consist partly of numbers that are less than 5 and partly numbers that is greater than 5. 6. Variance Analysis Variance analysis is a method for splitting the total variation of the data into meaningful components that measure different sources of variation.

For example, if an experiment of vines producing grapes is conducted, it was planted on equal size of plot and the yields per lot are recorded. The experimenter obtains 2 components, the first measuring the variation due to error and the second which measures the variation due to error plus any variation due to the different varieties of grapes. 7. Nonparametric Tests in Operations Management Decisions A nonparametric test does not require the population enable to correspond to a normal distribution, nor does the popular parameter need to be estimated.

Since patterns of people change drastically, nonparametric tests are very much applicable in operations management especially with a big organization. Works Cited Null Hypothesis. (n.d.). In wikipedia. Retrieved from http://en.wikipedia.org/wiki/Null_hypothesis Confidence Interval. (n.d.). In wikipedia. Retrieved from http://en.wikipedia.org/wiki/Confidence_interval Operations Management. (n.d.). In Business Dictionary. Retrieved from http://www.businessdictionary.com/definition/operations-management.html R. E.

Walpole (1982). Introduction to Statistics (3rd ed.). New York: MacMillan Publishing Co. Li Zongming (2009, September 30). The Importance of Hypothesis Testing in Quality Management. Quality Magazine. Retrieved from http://www.qualitymag.com/Articles/Web_Exclusive/BNP_GUID_9-5-2006_A_10000000000000671960