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Hypothesis testing is used to make decisions about a population based on the analysis of sample statistics. There are always two hypothesis statements which are mutually exclusive and complementary statements concerning the value of the population parameter of interest:

Null Hypothesis (H0):

An assumption regarding a population parameter of interest. This hypothesis always includes the equal sign as the null hypothesis is assumed to be true unless sample data produces evidence to the contrary.

Alternative Hypothesis (H1):

The alternative option available when the null hypothesis is rejected.

Three Types of Hypothesis Tests:

Lower-Tail Test Upper-Tail Test Two-Tailed Test

H0: ( ( (0 H0: ( ( (0 H0: ( = (0

H1: ( < (0 H1: ( > (0 H1: ( ( (0

Two-Sided Tests:

A Two-Tailed Test (TTT) is designed to detect a change in the population parameter of interest from some hypothesized value to some different value.

One-Sided Tests:

A Lower-Tail Test (LTT) is designed to detect a change in the population parameter of interest from some hypothesized value to some lower value.

An Upper-Tail Test (UTT) is designed to detect a change in the population parameter of interest from some hypothesized value to some greater value.

Test Statistics and Action Limits:

A test statistic is a sample statistic corresponding to the population parameter being tested. For example, when testing a hypothesis for a population mean, the corresponding test statistic (not standardized) is the sample mean. For any hypothesis test the general form of the standardized test statistic is given by:

Sample Statistic - Hypothesized Value Standard Deviation of Sample Statistic

The rationale is that assuming the null hypothesis is true, the sample statistic should be reasonably…...

...Hypothesis Testing Hypothesis testing is basically a process that uses statistical inference to test claims about population parameters. In hypothesis testing we begin by making a tentative assumption about a population parameter. This assumption is called the null hypothesis and is denoted by Ho. We then define another hypothesis, called the alternative hypothesis, which is the opposite of what is stated is the null hypothesis. The alternative hypothesis is denoted by Ha. The hypothesis testing procedure involves using data from a sample to test the competing claims indicated by the null and alternate hypotheses. Testing the hypothesis is similar to a criminal trail. Ho: The defendant is innocent Ha: The defendant is guilty Just as the defendant in a criminal trial is assumed to be innocent, the null hypothesis is assumed to be true and given the benefit of the doubt. The testimony and evidence obtained during the trial provide the sample information. If the sample information is consistent with the assumption of innocence, the null hypothesis that the defendant is innocent cannot be rejected. On the other hand, if the sample information is inconsistent with the assumption of innocence, the null hypothesis is rejected and action is taken based on the alternative hypothesis that the defendant is guilty. Developing Null and Alternative Hypotheses In some applications it may not be obvious how the null and alternative hypotheses should be......

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...able to fully understand hypothesis testing and the five steps involved in the complete process, one must first understand what a hypothesis and a hypothesis test is and why it is used. To begin with, a hypothesis, when involved in statistics, is an idea which could be set in the form of an assumption or a theory that shows the characteristics of a single or even multiple variables of a single or group of populations (Aron, Aron & Coups, 2009). These ideas or predictions need to be explored so as to give them validation, possibly creating further research, or these ideas need to be shown to be invalid, thus saving time by not putting more research into an idea that shows itself to be incorrect, however, sometimes an invalid result can create further research of another facet of the original idea set forth. Hypothesis testing is a process that uses statistical data in order to determine if an idea is able to be supported or warrants further research within a certain population that the idea or prediction seems to apply to, and is used by researchers (Aron et. al., 2009). There are five steps involved in this research process. The first step is to pose the question related to the idea or prediction as a logically formed statement called a research hypothesis. In addition to this statement, there is also a statement that is the complete opposite of the research hypothesis statement, called a null hypothesis statement (Aron et. al., 2009). Both these hypothesis statements are......

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...Sample Hypothesis Testing Paper RES/342 Two-Sample Hypothesis Research Question A company decides to purchase homes to rent out to their employees. They have to decide if purchasing homes in a rural area is cheaper than purchasing homes from the inner city. 15 miles from the center of the city is inner city and anything passed 15 miles is rural area. The mean house pricing in the urban area is $232,736 out of a sample size of 59 with a standard deviation of $48,651. The mean house pricing in the rural area is $206,183 out of a sample size of 46 with a standard deviation of $40,896. At the 0.05 significance level, the company assumes that urban area is higher than rural area. Formulating a Verbal and Numeric Hypothesis To formulate a verbal and numerical hypothesis statement one must determine which type of two-sample statistic test the problem describes. The statement indicates that one would perform a right-tailed test. The words “is higher than” indicates that the alternate hypothesis will have the greater than sign in it. The statement also indicates that the standard deviation is known. Using this knowledge one may begin to formulate a verbal hypothesis. The researchers will test the hypothesis statement and try to find sufficient evidence to support the null hypothesis. If the evidence is insufficient one will reject the null hypothesis. If the evidence is sufficient one may fail to reject the null hypothesis. Simply put one is trying to figure out if the......

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...Unit 4 – Hypothesis Testing & Variance Abstract There are two tests that are preformed following a two-tailed hypothesis test, using a .05 significance level. The first test is intrinsic by gender and the second is extrinsic variable by position type. This section will be taking a closer look at intrinsic satisfaction by gender and extrinsic satisfaction by position. Separate hypothesis test will be performed on both variances with the outcomes. Hypothesis Test #1 Looking at Intrinsic Satisfaction by Gender H0:Males= μ Females H1:Males= μ Females ∝ = .05 Significance level: 0.05 T statistic: 2.05 Critical T values: -1.98 and 1.98 P value: 0.04 Since the test statistics of 2.05 is greater than critical value of 1.98 we reject to reject the Ho. The decision made for the intrinsic job satisfaction survey, which intrinsic is when one does it for one’s satisfaction. The data says that it does not support the intrinsic Ho. The p value is less than the alpha. Managers for this business could use this information specifically to help drive the motivation of their employees. This information could show value in the growth of the company with having employees that enjoy their job and complete for their own satisfaction not for reasons such as outside rewards could say a lot about working for this company. If employees first enjoy their job this could mean greatness for the company, employees will strive to better the company and their......

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...Hypothesis Testing Opinions of Social Security System Probability and statistics August 1 2013 1. The Problem In an effort to design better advertising campaigns, the public relations department of the Social Security Administration conducted a survey to find out the opinions people in the United States have about the Social Security System. The public relations department collected and analyzed the survey data and claims that 40% of people in the United States think the Social Security system will have money available to provide the benefits they expect for their retirement. Also, they claim that the average age of people in the United States who would say yes to this question when asked is 60 years or older. The purpose of this study is therefore to examine and test the hypothesis of these claims and determine whether they can be supported or rejected for advertising purposes. 2. The Research Design and Hypothesis To test the hypothesis, a data table was collected from a survey adapted from Newsweek, by the public relations department of the Social Security Administration. The survey consisted of data from 32 adults ranging in age from 18 to 83. The study examines the two hypothesis by utilizing the classical method to construct a condition for testing the hypothesis claimed by the public relations department of the Social Security Administration. In this case, the null hypothesis is 40% of the people in the United States think the Social......

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...study is one store from each state’s capital plus one store from an average city in the state. What is still unknown is if any outliers would apply to each of the sample stores like many stores in our district have. As there is no way to know what these may be without contacting each store, the test data is just the average ACT for the first quarter of 2013. The Null Hypothesis from Corporate is that the Average Customer Transaction is $26.00. The Alternative Hypothesis is that our region has an ACT that is less than $26.00. This test uses twenty five points of data but the standard deviation is unknown so a t-test must be used. This would be a one-tailed test since the data that is of most importance is below the null of $26.00. The null hypothesis is H0: µ = $26.00 while the alternative hypothesis is H1: µ > $26.00. The alpha significance level is set at .05 or 5%. Following the Excel calculations, the t-test value is t = 0.894774 and the p value is -0.1899. Since the p value is lower than the significance level of .05, we reject the null hypothesis in favor of the alternative hypothesis which shows that the sample of Southeastern UPS Stores have average customer transaction is below the corporate standard of $26.00. The most significant issues with the data in cases such as this are that the customer base demographics are not included in our test or in the corporate office test. Too many other factors are ignored for the corporate statistic such......

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... Hypothesis Testing PSY/315 Jenna Griffin Amber Lupo Suppose that a doctor claims that 21 year olds have an average body temperature that is higher than the commonly accepted average human temperature of 98.6 degrees Fahrenheit. A simple random statistical sample of 25 people, each of age 21, is selected. The average temperature of the 21 year olds is found to be 98.9 degrees, with standard deviation of 0.6 degrees. The claim being investigated is that the average body temperature of 21 year olds is greater than 98.6 degrees. This corresponds to the statement x ≥ 98.6. The negation of this is that the population average is not greater than 98.6 degrees. In other words the average temperature is less than or equal to 98.6 degrees. In symbols this is x < 98.6. One of these statements must become the null hypothesis, and the other should be the alternative hypothesis. The null hypothesis contains equality. So for the above, the null hypothesis H0 : x = 98.6. It is common practice to only state the null hypothesis in terms of an equal’s sign, and not a greater than or equal to or less than or equal to. The statement that does not contain equality is the alternative hypothesis, or H1 : x >98.6. The statement of our problem will determine which kind of test to use. If the alternative hypothesis contains a "not equals to" sign, then we have a two tailed test. In the other two cases,......

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...Hypothesis Testing Paper Hypothesis testing in statistics goes beyond the traditional acceptances of trying to prove a hypothesis correct. Hypothesis testing is matter of accepting what has already been proven until another hypothesis is verified to be true. In the essay, an overview of the hypothesis testing process is described using a fictional example and numerical values to detail the process. The idea formed by the hypothesis, “online students have more stress than traditional on campus students”, is to reject the hypothesis that online college students experience less stress than on campus college students. This is in no way true findings; it is a fictional example to help walk the reader through the steps of hypothesis testing. Hypothesis testing is a king of research used to say how a certain topic of interest will end or how researchers think it will end in the environment. The testing will show that just because one forms an answer it does not prove that the answer is correct for there are many factors that could change the outcome, which is why researchers use probability rates of five or one percent. The null hypothesis endeavors to show that there is no variation between variables, or a single variable is no different from zero. It is surmised to be true until statistical evidence nullifies it for an alternative hypothesis. Null hypothesis is a hypothesis that the researcher endeavors to confute, reject, or nullify. The research hypothesis is the......

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...The steps in testing a research hypothesis There are a total of five steps that are used in testing a hypothesis and they are: “(1) Making assumptions, (2) Stating the research and null hypotheses and selecting (setting) alpha, (3) Selecting the sampling distribution and specifying the test statistic, (4) Computing the test statistic, and (5) Making a decision and interpreting the results.” (Boston University Metropolitan College, n.d., Para. 1). When beginning the process of creating a hypothesis to test, the first thing that must be done is to make assumptions about the type of sampling method that would be used, the level of measurement for the variable, including the sample size. The second step is then to state the research and null hypotheses and selecting the alpha. “We always state research hypotheses in terms of population parameters because we want to use sample statistics to estimate population parameters.” (Boston University Metropolitan College, n.d., Para. 5). After the research has been stated, then the next step is to complete the null hypothesis, which will contradict the research hypothesis. The third step in testing a hypothesis is to select the sampling distribution and to specify the test statistic. The fourth step is to compute the test statistic following the specified formula to be able to test the statistic. The fifth and final step is to make a decision and to interpret the results. This simply means that we are looking over the results and......

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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......

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...Hypothesis Testing Paper Michelle Ware Psy 315 July 6, 2015 Nancy Walker Hypothesis Testing Paper Criminal acts stemming from prejudice based on race, religion, sexual orientation, or ethnicity-frequently referred to as “hate violence”- have increased during recent years. (Barnes & Ephross, 1994) My hypothesis is the nature of hate attacks and victim’s responses. We can date back in American history the major importance of crime as a social problem. Society in America has been increasingly concerned about this problem and the victims experience with hate. This type of crime has generated the development of a numerous variety of victim service programs and research that will focus on victims instead of giving the criminals their five seconds of fame. “Hate violence crimes are those directed against persons, families, groups, or organizations because of their racial, ethnic, religious, or sexual identities or their sexual orientation or condition of disabilities. These crimes include arson of homes, businesses, and harassment, destruction of religious property, cross burnings, personal assaults, and homicides.” (Barnes & Ephross, 1994) It could be a difficult task to estimate the current prevalence of hate violence in the United States. With the help of media sources, there is a way to keep track and be more aware of these types of crimes. Focus group meetings, individual interviews, and questionnaires would be a way of sampling victims. Victims should...

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...Hypothesis Testing Tricia Gifford PSY/315 May 4, 2015 Karen Hoeve Hypothesis Testing Before a hypothesis test can be performed, it would be beneficial to have an understanding of what a hypothesis test is inclusive. A hypothesis is a declaration made in advance based on informal observation, a theory, or previous research, which is tested in a study. When this hypothesis declaration has been made, the hypothesis test can then be performed, which is a process for making a decision as to the outcome of a study supporting a particular theory or realistic innovation primarily thought to pertain to a population. In this hypothesis-testing scenario presented, a chosen research topic will be described along with its hypothesis statement concerning the topic. A population and its description will be determined and how the sampling method was obtained. The statistical technique will also be analyzed determining of the data. Research Issue The hypothesis test always starts out with a question regarding a subject of interest. The subject of interest is to determine if the suicide rate in the Pacific Northwest population is higher than the suicide rate in the South Midwest population. The states included in the Pacific Northwest are Idaho, Oregon, and Washington, and the states inclusive in the South Midwest are Arizona, New Mexico, and Texas. The populations are: 1) residents in the Pacific Northwest, and 2) residents in the South Midwest. ......

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...Hypothesis Testing Question for self-study: 1. Mary Arnold wants to use the results of a random sample market survey to seek strong evidence that her brand of breakfast cereal has a least 20% of the total market. Formulate the null and alternative hypothesis, using P as the population proportion. 2. The Federal Reserve Board is meeting to decide if it should reduce interest rates in order to stimulate economic growths. State the null and alternative hypothesis regarding economic growth that the board would formulate to guide its decision. 3. John Stull, senior vice president of manufacturing, is seeking strong evidence to support his hope that new operating procedures have reduced the percentage of under filled cereal packages from the Ames production line. State his null and alternative hypothesis and indicate the results that would provide strong evidence. 4. During 2000 and 2001 many people in Europe objected to purchasing food that was genetically modified, produced by farmers in the United States. The U.S. farmers argued that there was no scientific evidence to conclude that these products were not healthy. The Europeans argued products were not healthy. The Europeans argued that there still might be a problem with these foods. a. State the null and alternative hypotheses from the perspective of the Europeans. b. State the null and alternative hypotheses from the perspective of the U.S. farmers. 5. The 200- presidential election......

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...Regression Hypothesis Test Team A Res/342 February 23,2012 John Broy Regression Hypothesis Test Increasingly, the housing market has been in a slump. Relators as well as home owners are trying to find creative ways to get the most for their homes. Regression analysis is a statistical tool for the investigation of relationships between variables (). Team A will use the regression analysis procedure to develop a quantitative relationship between the price of the home and the size. The dependent variable is the price and the independent variable would be the square footage. Team A will formulate a hypothesis statement, interpret the results of the regression hypothesis, and explain the linear regression. The purpose of Team A’s research utilizing Real Estate Data sets provided by University of Phoenix is to observe if the size of the home has an effect on the price. Team A’s problem statement will evaluate if there is a direct correlation between the price of the home and the square footage. The research question Team A is trying to answer is; will the data provided show the difference in the price of the home and the square footage. The team will sample 105 homes priced from $125,000 to $345,000 and ranging from 1600 to 2900 square feet. The hypothesis is there a difference in the price for the square footage. Regression Analysis | | | | | | | | | | | | | | r² | 0.138 | n | 105 | | | | r | 0.371 | k | 1 | | | | Std.......

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...Nonparametric Hypothesis Testing RES/342 Nonparametric Hypothesis Testing During the course of the last three weeks, the team explored the hypothesis testing segment of statistics research. The first part of this assignment was the one sample hypothesis testing. The second was the two or more sample hypothesis testing, and finally in this third week, we will look at nonparametric hypothesis testing. This week’s project is a continuation of the previous projects and entails to build on the identical research question that we will frame a research hypothesis from the same provided data sets (Wage and Wage Earners) using ratio or interval numerical data; however, this week we will use a nonparametric hypothesis test to find our answer. In the next following paragraphs, the team will clearly affirm a hypothesis statement that will provide the base for our survey, perform a five-step hypothesis test on information concerning our choice and apply the concepts of nonparametric testing learned in this course, and describe how the results of our findings answer our research question. Finally, we will conclude this study with a brief summary that will examine the main points, the purpose, and conclusions of this final third week’s study on nonparametric testing. Perform the five-step hypothesis test on the data Nonparametric tests are statistical tests that analyze data that does not require assumptions about the distribution of shape of the population from......

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