Statistics 401 Mod 2 Case - Hypothesis Testing 1 Coursework

Statistics 401 Mod 2 Case - Hypothesis Testing 1 - Coursework Example Since then in the U.S. genetic engineering has expanded in various areas of food production. In 2006, among all countries of the world, United States alone grew 53% of genetically modified crop (Oak Ridge National Laboratory). The purpose of this study is to evaluate influence of GM food over non-GM food. In order to do so, this assignment has selected Tomatoes. It is claimed that genetically modified tomatoes show longer shelf lives than non-genetically modified tomatoes (Discovery). This assignment uses statistical design method to verify this claim. The design method is called hypothesis test. There are two different hypotheses; null hypothesis, and alternative hypothesis. If one hypothesis is true then the other hypothesis is false. In this design, null hypothesis is defined as Ho: The mean value of shelf lives of GM tomatoes is equal or greater than the mean value of shelf lives of non-GM tomatoes. The alternative hypothesis is defined as Ha: The mean value of shelf lives of GM tomatoes is less than the mean value of shelf lives of non-GM tomatoes. In a mathematical way, the test tends to satisfy the condition SL mean GM > = SL mean non-GM, where SL mean GM is the mean value of shelf lives of genetically modified tomatoes and SL mean non-GM is the mean value of shelf lives of non-genetically modified tomatoes. ... are less than       non-GM tomatoes non-GM shelf lives                   Hypothesis Evaluation against observations Acceptance of hypothesis Observations Ho Ha Ho Ha Test confirms null, Ho Null is TRUE Alternative is FALSE No Error Type I Error Test does not confirm null, Ho Null is FALSE Alternative is TRUE Type II Error No Error Type I error: Tomato growers do not buy GM plants and lose money from rotting tomatoes. Type II error: Tomato growers buy GM plants, which are more expensive than non-GM, but shelf lives do not increase. Tomatoes may be produced both from genetically modified or non-genetically modified plants. The study claims that shelf lives of GM tomatoes are greater than the shelf lives of non-GM tomatoes. Through statistical test it can be verified whether the distributions of shelf lives of GM and non-GM tomatoes differ from each another or not. This can be achieved through Chi-square test. The Chi-square test consists of (1) hypothesis formulation, ( 2) test design plan, (3) sample data analysis, and (4) result interpretation. The Chi-square test also assumes the following: GM tomatoes sampling is random; the population is10 times larger than the sample; the variable is categorical, and each level of the variable has at least 5 frequencies. The Chi-square study uses shelf lives values from GM tomatoes population and compares them to the shelf lives values of non-GM parameters. In Chi-square test, shelf lives of non-GM parameters are considered as expected values. The shelf lives of non-GM parameters include three levels: (1) mean value of the population, (2) greater than the mean value, and (3) less than the mean value. If the GM tomatoes do not increase the shelf lives, then the study will duplicate the non-GM results. On the contrary, if the GM