...Elements of a Test of Hypothesis 1. Null Hypothesis (H0 ) - A statement about the values of population parameters which we accept until proven false. 2. Alternative or Research Hypothesis (Ha )- A statement that contradicts the null hypothesis. It represents researcher’s claim about the population parameters. This will be accepted only when data provides sufficient evidence to establish its truth. 3. Test Statistic - A sample statistic (often a formula) that is used to decide whether to reject H0 . 4. Rejection Region- It consists of all values of the test statistic for which H0 is rejected. This rejection region is selected in such a way that the probability of rejecting true H0 is equal to α (a small number usually 0.05). The value of α is referred to as the level of significance of the test. 5. Assumptions - Statements about the population(s) being sampled. 6. Calculation of the test statistic and conclusion- Reject H0 if the calculated value of the test statistic falls in the rejection region. Otherwise, do not reject H0 . 7. P-value or significance probability is defined as proportion of samples that would be unfavourable to H0 (assuming H0 is true) if the observed sample is considered unfavourable to H0 . If the p-value is smaller than α, then reject H0 . Remark: 1. If you fix α = 0.05 for your test, then you are allowed to reject true null hypothesis 5% of the time in repeated application of your test rule. 2. If the p-value of a test is 0.20 (say) and you reject H0 then, under...
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...Hypothesis Testing Paper A hypothesis is a prediction, a tentative explanation for an observance, phenomenon, or scientific problem. A researcher further investigates the hypothesis by testing (“hypothesis,” 2002). More specifically, the way a researcher tests a hypothesis is by hypothesis testing. “Hypothesis testing is a procedure for deciding whether the outcome of study (results for a sample) supports a particular theory or practical innovation, which is thought to apply to a population” (Aron, Aron, & Coups, 2009, p. 107). In this paper, team E chose to describe the results of a hypothesis test on the 401k plan for two different companies. Team E formulated a numerical and verbal hypothesis statement regarding the 401k plans of two companies, and performed the five-step hypothesis. Finally, team E describes the results and explains how one can use hypothesis testing to evaluate solutions, which may help assist in the decision of which company has a better 401k plan. Benefits are not just for the end of one’s career even though typically many individuals think of benefits as basic insurance coverage. A respectable benefit plan can take into account many additional perks that offer true substantial gains in relation to the competition. As a result one may seek employment with a company whose 401k plan can be of assistance to allow one to begin building a tax-deferred retirement nest egg early. Take into account the amount the company will match, if any, and the maximum...
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...Chapter 9 Hypothesis Tests Solutions: 6. a. H0: μ ≤ 1 Ha: μ > 1 b. Claiming μ > 1 when it is not. This is the error of rejecting the product’s claim when the claim is true. Concluding μ ≤ 1 when it is not. In this case, we miss the fact that the product is not meeting its label specification. H0: μ ≤ 8000 Ha: μ > 8000 b. Research hypothesis to see if the plan increases average sales. The label claim or assumption. c. 7. a. Claiming μ > 8000 when the plan does not increase sales. A mistake could be implementing the plan when it does not help. Concluding μ ≤ 8000 when the plan really would increase sales. This could lead to not implementing a plan that would increase sales. z= x − μ0 = 26.4 − 25 6 / 40 = 1.48 c. 10. a. b. σ/ n Upper tail p-value is the area to the right of the test statistic Using normal table with z = 1.48: p-value = 1.0000 - .9306 = .0694 Using Excel: p-value = 1 - NORMSDIST(1.48) = .0694 c. d. p-value > .01, do not reject H0 Reject H0 if z ≥ 2.33 1.48 < 2.33, do not reject H0 11. a. b. z= x − μ0 σ/ n = 14.15 − 15 3 / 50 = −2.00 Because z < 0, p-value is two times the lower tail area Using normal table with z = -2.00: p-value = 2(.0228) = .0456 9-1 Chapter 9 Using Excel: p-value = 2*NORMSDIST(-2.00) = .0456 c. d. p-value ≤ .05, reject H0 Reject H0 if z ≤ -1.96 or z ≥ 1.96 -2.00 ≤ -1.96, reject H0 15. a. H0: μ ≥ 1056 Ha: μ < 1056 b. z= x − μ0 = 910 − 1056 1600 / 400 = −1.83 σ/ n Lower tail...
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...Question 1: Hypothesis Test for US Public Transportation Year | Percent of Public Transportation | 1997 | 4.6 | 1999 | 4.9 | 2001 | 4.7 | 2003 | 4.4 | 2005 | 4.7 | 2006 | 4.8 | 2007 | 4.9 | 2008 | 5.0 | 2009 | 5.0 | 1/ Less than 5% of US citizens use public transportation according to several websites of U.S. Departments of Transportation Survey. = 4.778 SD = 0.199 n = 9 The test statistic: t= = = 71.276 We have enough evidence to reject H0 Thus, we have sufficient evidence to prove that less than 5% of US citizens use public transportation. Base on the data, in 2008 and 2009, the percentage of people who used public transportation was the highest (5%). Because of the development of the world in general and the U.S in particular, people in U.S prefer using bus, streetcar, subway, railroad, and elevated trains. In 1999 and 2007, there had high rate of proportion of residence using public transportation (4.9%) perhaps because of the population explosion. There were also 4.6% in 1997, 4.7% in 2001 and in 2005, and 4.8% in 2006 respectively. Resource: U.S. Department of Transportation Research and Innovative Technology Administration Bureau of Transportation Statistics National Transportation Statistics http://www.bts.gov/publications/national_transportation_statistics/2010/html/table_01_38.html Question 2: Multiple Regressions We take the data from OSEVEN Company (www.oseven.vn) The result of the Regression for the percentage: ...
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...Analyzing and Improving a Test Using Statistics Maurice Isaiah McCall Introduction: Hypothetical Psychology Test This hypothetical psychology test consisted of five test questions. These test items and questions were not unambiguous and there were no evidence of instructions or explanations given for either test question. In our text it was mentioned there were several steps the admitter need to take before administering, analyzing and improving a test or assessment. There was no evidence these test questions were constructed and that it matched any objective. However the guidelines for packaging the test states [items need to be in a similar format, grouped together, test items need to be arranged from easy to hardest, have items properly spaced as well as checking for directions, clarity and proofreading the test before it is reproduced and distributed]. (Kubiszyn & Borich, p. 223 & 224). It is very obvious these test questions lack validity and were poorly written, these test questions were more in line with the intended audience partaking in a survey. A survey question refers to the quantitative research or a statistical survey, for the sole purpose of collecting quantitative information about the general population or a product. Each of these test questions contained its own set of problems and uniqueness about them. For example every given answer had an asterisk mark beside of it and for any test taker this is a distraction, and the test itself was not formatted...
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...Formative and Summative Assessment (Journal 1) By: Cinthia Herrera Edu: 645 Learning and Assessment for the 21st Century Instructor: Amy Peterson July 29, 2013 In comparison of the formative and summative assessment is that, they are both part of the broad assessment process which may span for days, weeks, a full semester, an entire school year or even longer. When it comes to formative and summative assessment teachers traditionally have not been well trained and this is because they believe these activities are supplemental or peripheral to the instruction process (Kubiszyn & Borich, 2013). These two assessments are only tools and can both be poorly designed, misused unintentionally, and impair their usefulness if abused intentionally. Both, Formative and summative assessment can be referred to as single measures that yield results at a single point in time in a classroom, and they are both a part of an assessment process to help make educational decisions (Kubiszyn & Borich, 2013). In contrast summative assessment are lengthy and are used to assign grades, evaluate curriculum effectiveness, assess annual gains in student, school, and district academic improvement. This assessment is good to inform about broad achievement trends after instruction has been completed. Summative is not a useful tool if the purpose of testing is to evaluate the effectiveness of instruction on a day-to-day basis. It is also not designed to be sensitive to small specific changes...
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...Statistics: Highly Informative Latosha Greer BUS308: Statistics for Managers Instructor Hayes June 1, 2014 In this essay I am aim to discuss the differences between descriptive statistics and Inferential statistics and the reasons why we use them. I will also discuss hypothesis development and testing, when to select the appropriate statistical test, and how to evaluating statistical results. In this class I learned the difference between descriptive statistics and inferential statistics. We use descriptive statistics to measure and analysis data. There are a number of reasons why we use Descriptive statistics. We use it, because Descriptive statistics numerical summaries measure the central tendency of a data set, it can include graphical summaries that show the spread of the data, and they provide simple summaries about the sample that help interpret and analyze data. First, there are a number of reasons why we use descriptive statistics we use it because descriptive statistics numerical summaries that either measure the central tendency of a data set. In business therefore descriptive statistics helps in making conclusions about various issues and therefore helps in making decision. Description statistics is the first step in analyzing data before making inferences of data, therefore it is important in analyzing any data collected that will help in describing the characteristics of data collected. There are three measurements that we tend to use. One measurement...
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...deviation of 4.45 pages. (a) At the .01 level of significance, is the true mean greater than 10? (Please show answer in Excel format to find the right-tail p-value. Answer The test statistic used is H0: True population mean ( =10 H1: True population mean ( >10 The test statistic used is [pic] Decision rule: Reject the null hypothesis, if the calculated value of test statistic is greater than the critical value of t. Details |t Test for Hypothesis of the Mean | | | | |Data | |Null Hypothesis μ= |10 | |Level of Significance |0.01 | |Sample Size |35 | |Sample Mean |14.44 | |Sample Standard Deviation |4.45 | | | | |Intermediate Calculations | |Standard Error of the Mean |0.752187287 | |Degrees of Freedom |34 | |t Test Statistic |5.902785222 | | | | |Upper-Tail Test | | |Upper Critical Value...
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...Institute of Management Sciences Peshawar Bachelors in Business Studies Course Plan Course Title: Statistics for Business Instructor: Shahid Ali Contact Email shahid.ali@imsciences.edu.pk Semester/Duration: 16 Weeks Course objectives : To introduce students to the concepts of statistics and to equip them with analytical tools to be used in business decision making. The course is intended to polish the numeric ability of the students to identify business problems, describe them numerically and to provide intelligible solutions by data collection and inferential principles. Course pre-requisites Intermediate statistics Attendance Policy: Late arrivals are highly discouraged. Any student coming late to a class late by 5 minutes after the scheduled start time will be marked as absent for the day. The teacher reserves discretion, however, to allow or disallow any student, to sit in the class in case of late arrivals. Attendance is not be entertained once the attendance register is closed. Class Project Students will be divided in groups for a class project. Each group will have to nominate a group leader. The details of the project will be made available to the group leader. Class Presentations Each student will have to make at least one individual presentation and one group presentation in the class. The group presentation will be on the project explained earlier. The individual presentations will...
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...case Dr. Nefario randomly assigns each person that participated in the study to one of the two groups. One of the groups is a group that is allowed to sleep for 8 hours the night before the test and another group is a group that is allowed to sleep for 2 hours, so, in this case Dr. Nefario run a between subject experimental design. This random assignment is essential because it gives each condition to has an equal probability of being affected by participates’ differences. In this case, Dr. Nefario wants to see if the median response time is different between the two groups. Median is the middle score of set of data. We can find the median...
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...analysis with statistics has got less to do with numbers, and more to do with rules for arranging them. It even lets you create some of those rules yourself, so instead of looking at it like a lot of memorization, it's best to see it as an extension of the research mentality, something researchers do anyway (i.e., play with or crunch numbers). Once you realize that YOU have complete and total power over how you want to arrange numbers, your fear of them will disappear. It helps, of course, if you know some basic algebra and arithmetic, at a level where you might be comfortable solving the following equation There are three (3) general areas that make up the field of statistics: descriptive statistics, relational statistics, and inferential statistics. 1. Descriptive statistics fall into one of two categories: measures of central tendency (mean, median, and mode) or measures of dispersion (standard deviation and variance). Their purpose is to explore hunches that may have come up during the course of the research process, but most people compute them to look at the normality of their numbers. Examples include descriptive analysis of sex, age, race, social class, and so forth. 2. Relationalstatistics fall into one of three categories: univariate, bivariate, and multivariate analysis. Univariate analysis is the study of one variable for a subpopulation, for example, age of murderers, and the analysis is often descriptive, but you'd be surprised how many advanced statistics can be computed...
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...Regression Analysis Paper only MTH 233 Learning Team Assignment: Hypothesis Testing and Regression Analysis Presentation ----------------------------------------------- MTH 233 Learning Team Assignment Hypothesis Testing and Regression Analysis Presentation For more classes visit www.snaptutorial.com Resources: University Library and the Internet Select a research issue, problem, or opportunity facing a Learning Team member’s organization to examine using hypothesis testing and a regression analysis on the collected data. Write a 1,050- to 1,750-word paper describing a new hypothesis test using a different statistic (e.g., large sample size, small sample size, means and/or proportions, one- and two-tailed tests) to perform on that data. Formulate a new hypothesis statement and perform the five-step hypothesis test on the data. Describe the results of the tests. Interpret the results of the regression analysis, state the limitations of the analysis, and describe the significance of the results to the organization. Be sure to attach the results of the regression analysis created in Microsoft® Excel to your paper. Present the results to the class in a 10-minute PowerPoint® presentation ----------------------------------------------- MTH 233 Week 2 Individual Assignment Individual Assignment 1 For more classes visit www.snaptutorial.com Resources: Ch.1 & 2 of Elementary...
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...samples, the client could quickly learn whether the process was operating satisfactorily. When the process was not operating satisfactorily, corrective action could be taken to eliminate the problem. The design specification indicated that the mean for the process should be 12. The hypothesis test suggested by Quality Associates follows: H0: μ=12 Ha: μ≠ 12 Corrective action will be taken when H0 is rejected. Samples collected during the first day of operation of the new statistical process-control procedure are in the file Quality.xls. The URL to this dataset is A. Conduct a hypothesis test for each sample at the .01 level of significance and determine what action, if any should be taken, Answer H0: μ=12 Ha: μ≠ 12 Test Statistic used is Z test Decision rule: Reject null hypothesis, if the value of test statistic is greater the critical value. Details Sample 1 Z Test of Hypothesis for the Mean Data Null Hypothesis μ= 12 Level of Significance 0.01 Population Standard Deviation 0.21 Sample Size 30 Sample Mean 11.96 Intermediate Calculations Standard Error of the Mean 0.038340579 Z Test Statistic -1.078057097 Two-Tail Test Lower Critical Value -2.575829304 Upper Critical Value 2.575829304...
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...snaptutorial.com PSYCH 625 Week 1 Individual Assignment Basic Concepts in Statistics Worksheet PSYCH 625 Week 1 Individual Assignment Reliability and Validity Matrix PSYCH 625 Week 1 Individual Assignment Time to Practice – Week One PSYCH 625 Week 2 Individual Assignment Time to Practice – Week Two PSYCH 625 Week 2 Learning Team Assignment Statistics Project Import Data Into IBM ® SPSS ® Software PSYCH 625 Week 3 Individual Assignment Time to Practice – Week Three PSYCH 625 Week 3 Learning Team Assignment Hypothesis Testing Problem Worksheet PSYCH 625 Week 3 Learning Team Assignment Statistics Project Descriptive Statistics PSYCH 625 Week 4 Individual Assignment Time to Practice – Week Four PSYCH 625 Week 4 Learning Team Assignment Statistics Project Comparing Means PSYCH 625 Week 5 Individual Assignment Programmatic Assessment Time to Practice – Week Five PSYCH 625 Week 5 Learning Team Assignment Statistics Project Correlations PSYCH 625 Week 6 Individual Assignment Overview of Important Statistical Tests PSYCH 625 Week 6 Learning Team Assignment Statistics Project Presentation ----------------------------------------- PSYCH 625 Week 1 Individual Assignment Basic Concepts in Statistics Worksheet For more classes visit www.snaptutorial.com Complete the following questions. Be specific and provide examples when relevant. Cite any sources consistent with APA guidelines. What are statistics and how are they used in the behavioral sciences? Your answer should be...
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...the following variables (all measured in billions USD) and estimate the corresponding model (Model 1):(Use α=0.05 for references) Yt: Defense budget outlay for year t X2t: GNP for year t X3t: US military sales in year t X4t: Aerospace industry sales in year t D1t: Dummy variable presenting the military conflict involving more than 100,000 troops; D1t=1 if more than 100,000 troops are involved and equal to 0 if fewer than 100,000 troops are involved. |Dependent Variable: Y Sample: 1962 1981 | |Method: Least Squares Included observations: 20 | |Variable |Coefficient |Std. Error |t-Statistic |Prob. | |C |21.40251 |1.496947 |14.29744 |0.0000 | |D1 |-48.21987 |6.871544 |-7.017328 |0.0000 | |X2 |0.013879 |0.003207 |4.328062 |0.0008 | |X3 |0.073146 |0.203805 |0.358902 |0.7254 | |X4 |1.389753 |0.130197 |10.67423 |0.0000 | |X4*D1 |1.540792 |0.325005 |4.740818 |0.0004 | |X2*D1 |0.022406 |0.005781 |3.876038 |0.0019...
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