Week_5_Qnt_561

Executive Summary Making decisions require the individual to select single alternative from a number of alternatives. Generally a person is making decision without knowing whether it is correct or not; it is based on the incoherent information. Thus understanding of what decision-making involves with the use of hypothesis testing method will aid to produce accurate decisions (Harris, 2009). This paper will discuss the important of hypothesis testing in decision-making process. The goal of hypothesis testing is provide the truth and assist the individual to make valid and reliable decision. More accurately the researcher should have two hypotheses known as null hypothesis and alternative hypothesis. Researcher can often use one sample test of hypothesis to determine whether the hypothesis is believable and should not be rejected or it is unreasonable and should be rejected. A two- sample test of hypothesis is often used when the researcher want to answer the question about the mean where the data collected from two random samples of observations. One and Two- Sample Test of Hypothesis In research experimentation, researcher seek to uncover the verifiable truth about the world around them and then gather those evidence into theories that interpret the connection between the facts. From the observations and the data they obtain, researchers try to clarify an observation or event using information that is presently available. The language of statistic describe hypothesis as the assumption about population parameter (Lind, Marchal, & Wathen, 2008). Parameter is the characteristic of the population, like its variance or mean. Hypothesis testing is a scientific method to examine data, provides a foundation for taking theories or ideas, and aid the decision making process (Encyclopedia of Business, 2010). The main goal of hypothesis testing is to determine whether the hypothesis is reasonable statement and should not be rejected or it is unreasonable and should be rejected. Rejecting or disproving one of the models will finally be left with one that has not been disproven. The five steps process for hypothesis testing • State the null hypothesis and alternative hypothesis. The null hypothesis is a conditional statement that will be tested. However accepting and recognizing the null hypothesis does not mean it is true. The alternative hypothesis is revised or new ideas about a current situation based on the fact that the current idea is incorrect. In the same way, rejecting the null hypothesis does not prove the alternative hypothesis. In statistic, the null hypothesis is denoted with H0 symbol whereas the alternative hypothesis symbol is H1 (Investopedia, 2010). The table below demonstrates three sets of hypothesis. The population mean symbol is μ to describe the value of M and the symbol ≠ means not equal. Set Null hypothesis Alternative hypothesis Number of tails 1 μ = M μ ≠ M 2 2 μ > M μ < M 1 3 μ < M μ > M 1 • Specify the significant level. The significance level of a test is the chances of rejecting the a null hypothesis when it is true known as type I error and when accepting the null hypothesis when it is wrong the researcher committing another type of error called type II error (Lind, Marchal, & Wathen, 2008). • To calculate the test statistic, the researcher decision is based on sample values whether to accept or reject the null hypothesis. • Formulate the decision rule. A decision rule is a statement of the specific conditions under which the null hypothesis is rejected and the conditions under which it is not rejected. • Make a decision regarding the null hypothesis based on the sample information. Define the results. One- Sample Test of Hypothesis One-sample tests are used if the population parameter is different from specified value (Gallagher, 1997). In an effort to make decisions about the population based from the sample observation. The researcher can make decision based from his or her assumption using one- sample test of hypothesis. • Testing for population mean with known population standard deviation. Example Lakwanta Steel Company manufactures and assembles desks and other office equipment at several plants in Scranton, Pennsylvania. The weekly production of the Model A301 desk at the Fredonia Plant follows the normal probability distribution with a mean of 200 and a standard deviation of 16. Because of market expansion, new production process has been introduced and new employees hired. The upper level management of the company would like to investigate and examine whether there has been a change in the weekly production of the Model A301 desk. Step 1: State the null hypothesis and the alternate hypothesis. H0: μ = 200 H1: μ ≠ 200 (Note: keyword in the problem “has changed”) Step 2: Select the level of significance. α = 0.01 as stated in the problem Step 3: Select the test statistic. Use Z-distribution since σ is known Step 4: Formulate the decision rule Reject H0 if |Z| > Zα/2 Step 5: Make a decision and interpret the result. Because 1.55 does not fall in the rejection region, H0 is not rejected. We conclude that the population mean is not different from 200. So we would report to the vice president of manufacturing that the sample evidence does not show that the production rate at the Scranton Plant has changed from 200 per week. The Two –Sample Test of Hypothesis The two- sample hypothesis testing is a statistical analysis used to test if there is dissimilarity or difference between two means from the two different populations. An example of two- sample test hypothesis test for means: • The time spent in library is the response variable. • The explanatory variable dividing the sample into two groups is the variable “ what was the main purpose of the people who visit the library' Business or personal' • Is there a difference in time spent in library by purpose of visit' Statistic for two samples Business Personal n = 95 n = 218 Mean = 48.98 Mean = 37.78 Standard deviation = 48.30 Standard deviation = 35.945 1. Assumption 2. Hypothesis - Null hypothesis H0: μ1 = μ 2 and the alternative hypothesis Ha: μ 1 ≠ μ 2.The level of significance - The chances of error in making decision to reject the null hypothesis. The significance level is equal to 0.05. 4. Test statistic - The t equals actual difference minus hypothesis difference over standard error of difference. Standard error of difference 5. P- value - The t value is equal to -2.028 with 94 df .The t value is less than t .010 and greater than t.025 for both 80 and 100 df. The probabilities are double since it is two- tailed test. The p- value is greater than 0.020 and less than 0.050. 6. Conclusion - The p value is less than the level of significance α = 0.05, therefore reject the null hypothesis and conclude that the population mean times spent in the library differ for types of users. References Harris, R. (2009). What is Decision Making' Virtual Salt. Retrieved from http://www.virtualsalt.com/crebook5.htm Hypothesis Testing. (2011). In Encyclopedia of Business, 2nd ed.. Retrieved from http://www.referenceforbusiness.com/management/Gr-Int/Hypothesis-Testing.html Lind, D. A., Marchal, W. G., & Wathen, S. A. (2008). Statistical Techniques in Business Economics. Retrieved from. https://ecampus.phoenix.edu/content/eBookLibrary2/content/eReader.aspx Null Hypothesis. (2010). In Investopedia. Retrieved from http://www.investopedia.com/terms/n/null_hypothesis.asp