Get the full course at: http://www.MathTutorDVD.com The student will learn how to write the null and alternate hypothesis as part of a hypothesis test in statistics. We will work several examples so that the student gains an understanding of how to work hypothesis testing problems step-by-step.
Views: 793787 mathtutordvd
The simplest and most effective rule to correctly setting up the null and alternate hypotheses. Follow this step-by-step process and you will never get it wrong! This is a 7 minute lecture on the fool-proof rules to setting up the null and alternate hypotheses in Statistics. **** Come and check out my complete and comprehensive course on HYPOTHESIS TESTING! Click on the link below for a FREE PREVIEW and a MASSIVE discount (only for my Youtube students): https://www.udemy.com/simplestats/?couponCode=123 This is a complete course that covers all the topics (such as the central limit theorem, p-values, hypothesis tests using proportions, and so much more) in a structured, step-by-step manner, coupled with a bucket load of practice exam questions and video worked solutions. I assume the viewer has zero background in statistics. You also get to post questions in the discussion forum and I will answer them right away! https://www.udemy.com/simplestats/?couponCode=123 **** SUBSCRIBE at: https://www.youtube.com/subscription_center?add_user=quantconceptsedu **** Check out our other videos! Watch my complete 40 min lecture on Simple Regressions: https://www.youtube.com/watch?v=38iNlkzF1sE Simple Introduction to Hypothesis Testing: http://www.youtube.com/watch?v=yTczWL7qJ-Y A Simple Rule to Correctly Setting Up the Null and Alternate Hypotheses: https://www.youtube.com/watch?v=R2hxisYFKxM&feature=youtu.be The Easiest Introduction to Regression Analysis: http://www.youtube.com/watch?v=k_OB1tWX9PM Super Easy Tutorial on Calculating the Probability of a Type 2 Error: https://www.youtube.com/watch?v=L9rX8kTd8PI&feature=youtu.be ** Keywords: statistics, statistics help, statistics tutor, statistics tuition, hypothesis testing, regression analysis, university help, stats help, simple regression, multiple regression, econometrics, null hypothesis, alternate hypothesis, alternative hypothesis, stats tutor, study help
Views: 65846 Dave Your Tutor
Examples of how to write null and alternative hypotheses. View more lessons or practice this subject at http://www.khanacademy.org/math/ap-statistics/tests-significance-ap/idea-significance-tests/v/examples-of-null-and-alternative-hypotheses?utm_source=youtube&utm_medium=desc&utm_campaign=apstatistics AP Statistics on Khan Academy: Meet one of our writers for AP¨_ Statistics, Jeff. A former high school teacher for 10 years in Kalamazoo, Michigan, Jeff taught Algebra 1, Geometry, Algebra 2, Introductory Statistics, and AP¨_ Statistics. Today he's hard at work creating new exercises and articles for AP¨_ Statistics. Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help! Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc
Views: 55695 Khan Academy
Watch more of this topic at ► http://bit.ly/28Rs0V7 Download this PDF: http://bit.ly/28QriUe GET MORE CLUTCH! VISIT our website for more of the help you need: http://bit.ly/28StHAV SUBSCRIBE for new videos: http://cltch.us/1axA33X --- LET'S CONNECT! Facebook: http://cltch.us/1JLgiSZ Twitter: http://cltch.us/1NLcKpu Instagram: http://cltch.us/1If5pb7 Google+: http://cltch.us/1E34o85 Clutch Prep = Textbook specific videos to help you pass your toughest science classes.
Views: 5151 Clutch Prep
How to state the null hypothesis in easy steps.
Views: 65957 Stephanie Glen
In this video we examine hypothesis tests, including the null and alternative hypotheses. We take a look at a few different examples, with a focus on two-tailed tests in this video. Null hypothesis Alternative hypothesis H0 H1 Video Transcript: In this video we'll take a look at null and alternative hypotheses. Now the null hypothesis means there's no effect, or nothing happened, or there's no difference. The null hypothesis is often represented by H Sub zero. And it makes a statement about the population, not the sample. So in other words we put population values or symbols in our null hypothesis. Now the alternative hypothesis is really the opposite. It states or it means that there was an effect, or something happened, or there was a difference. The alternative hypothesis is often represented by H sub 1 or H sub A, and it also makes a statement about the population, not the sample. So if we take a look at these two side-by-side, once again, in review, the null is stated by H sub 0 the alternative is H sub 1 or H sub A. The null basically states nothing happened, and look at the opposite here, the alternative states something happened. Or the null can state no effect, the alternative states there was an effect. And, finally, the null can state no difference effectively, and the alternative would state the opposite, there was a difference. And once again both hypotheses refer to the population. Let's go ahead and take a look at an example using the Pearson correlation or Pearson's r. Now correlation measures the degree of the linear relationship, if there's any at all, between two variables, and it's known as Pearson's r. Let's go and take a look at the null and alternative hypotheses for correlation, or fir Pearson's r here. In words the null would state there is not a relationship between the two variables in the population. The alternative would state the opposite: it would state there is a relationship between the two variables in the population. Notice how the null states no effect, or there's no relationship, whereas the alternative states there is an effect, or there is a relationship. Using symbols we could say the following: the null, and that little thing that looks like a p there, that stands for rho, and it's the correlation in the population. So we would say null rho x,y equals 0 and then the alternative would say rho x,y does not equal zero. Or, in other words, the null would state there's no correlation between x and y, two variables in the population, whereas the alternative would state there is a correlation between the two variables, x and y, in the population. And 0 here means no relationship in correlation. So when the null says it's equal to 0, it's saying there's no relationship. When the alternative says it's not equal to 0, it stating there is a relationship. So, in review, the null states there's no effect or zero relationship, whereas the alternative states there is an effect, or a non-zero relationship. Now hypotheses need to be mutually exclusive and exhaustive. Exclusive means there's no overlap between the null and the alternative. And if you look at our two statements up above, where it says rho x,y equals 0, and rho x,y does not equal zero, notice that those do not overlap at all, equals and not equals are completely non overlapping. It's either 0, which is the null in that case, or it's not zero, which is the alternative. So they're completely exclusive, they do not overlap. And then exhaustive means they must cover, or exhaust, all possibilities, the null and alternative when taken together. And notice that they do, as every possible value for Pearson's r is either 0 or not 0, so it does exhaust all possibilities. So once again it’s exclusive, because they don't overlap, and it's exhaustive, because they cover all possibilities. Now notice how the alternative has a not equal sign, implying that the alternative hypothesis can be either greater than zero, or less than zero, or in other words correlation can be positive or negative. This is known as a two-tailed test, since the alternative hypothesis consists of two possibilities, either greater than zero or less than zero. Alternatively, one-tailed tests can also be used in hypothesis testing, and we'll examine one-tailed tests in another video.
Views: 39294 Quantitative Specialists
In this video we see 6 example of writing null and alternative hypothesis including equal to, less than, greater than, is at least, is no more than, and more than half.
Views: 109 Emporium Mathematics
This video demonstrates how to determine the null and alternative hypothesis, id & dd, 1 or 2 tailed test.
Views: 128 Moore Statistics
How to state the null hypothesis and the alternative hypothesis, and how to tell the type of test
Views: 1799 Nickie Christensen
There are four steps in data-driven decision-making. First, you must formulate a hypothesis. Second, once you have formulated a hypothesis, you will have to find the right test for your hypothesis. Third, you execute the test. And fourth, you make a decision based on the result. Let’s start from the beginning. What is a hypothesis? Though there are many ways to define it, the most intuitive I’ve seen is: “A hypothesis is an idea that can be tested.” This is not the formal definition, but it explains the point very well. So, if I tell you that apples in New York are expensive, this is an idea, or a statement, but is not testable, until I have something to compare it with. For instance, if I define expensive as: any price higher than $1.75 dollars per pound, then it immediately becomes a hypothesis. Alright, what’s something that cannot be a hypothesis? An example may be: would the USA do better or worse under a Clinton administration, compared to a Trump administration? Statistically speaking, this is an idea, but there is no data to test it, therefore it cannot be a hypothesis of a statistical test. Actually, it is more likely to be a topic of another discipline. Conversely, in statistics, we may compare different US presidencies that have already been completed, such as the Obama administration and the Bush administration, as we have data on both. Generally, the researcher is trying to reject the null hypothesis. Think about the null hypothesis as the status quo and the alternative as the change or innovation that challenges that status quo. In our example, Paul was representing the status quo, which we were challenging. Connect with us on our social media platforms: Website: https://bit.ly/2TrLiXb Facebook: https://www.facebook.com/365datascience Twitter: https://twitter.com/365datascience LinkedIn: https://www.linkedin.com/company-beta/18061054/ Google+: https://plus.google.com/114636546494634370189/ Prepare yourself for a career in data science with our comprehensive program: https://bit.ly/2HnysSC Get in touch about the training at: [email protected] Comment, like, share, and subscribe! We will be happy to hear from you and will get back to you!
Views: 27930 365 Data Science
Demonstrates the basics of hypothesis testing using the P-value method: find the test statistic which in turn gives us the P-value, then compare the P-value to the level of significance (alpha) to determine whether or not the Null Hypothesis is rejected or not. PLEASE READ!! I did not make a mistake by showing .0045 as the area (probability) for 2.61. Look carefully at my picture. I have shaded to the **RIGHT** of 2.61, not to the left. If you look up 2.61 on your table and see .9955 your table is assuming you want the area shaded to the LEFT of 2.61. Again, I shaded to the RIGHT of 2.61. I hope that makes sense!
Views: 1048805 poysermath
Hypothesis Testing and P-values Practice this yourself on Khan Academy right now: https://www.khanacademy.org/e/hypothesis-testing-with-simulations?utm_source=YTdescription&utm_medium=YTdescription&utm_campaign=YTdescription Watch the next lesson: https://www.khanacademy.org/math/probability/statistics-inferential/hypothesis-testing/v/one-tailed-and-two-tailed-tests?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics Missed the previous lesson? https://www.khanacademy.org/math/probability/statistics-inferential/margin-of-error/v/margin-of-error-2?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predictions, testing, and analyzing. Our lives are full of probabilities! Statistics is related to probability because much of the data we use when determining probable outcomes comes from our understanding of statistics. In these tutorials, we will cover a range of topics, some which include: independent events, dependent probability, combinatorics, hypothesis testing, descriptive statistics, random variables, probability distributions, regression, and inferential statistics. So buckle up and hop on for a wild ride. We bet you're going to be challenged AND love it! About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to KhanAcademy’s Probability and Statistics channel: https://www.youtube.com/channel/UCRXuOXLW3LcQLWvxbZiIZ0w?sub_confirmation=1 Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy
Views: 2129088 Khan Academy
Get this complete course at http://www.MathTutorDVD.com In this lesson, we will discuss the very important topic of p-values in statistics. The p-value is a calculation that we make during hypothesis testing to determine if we reject the null hypothesis or fail to reject it. The p-value is calculated by first finding the z test statistic. Once this is known we then need to find the probability of our population having a value more extreme than the test statistic. This is done by looking up the probability in a normal distribution table. We then interpret the results by comparing the p-value to the level of significance. -----------------
Views: 496107 mathtutordvd
Get the full course at: http://www.MathTutorDVD.com The student will learn the big picture of what a hypothesis test is in statistics. We will discuss terms such as the null hypothesis, the alternate hypothesis, statistical significance of a hypothesis test, and more. In this step-by-step statistics tutorial, the student will learn how to perform hypothesis testing in statistics by working examples and solved problems.
Views: 1319454 mathtutordvd
4 Keys to Understanding the Alternative Hypothesis and a technique for determining whether a 1-tailed (1-sided) test is left-tailed or right-tailed.
Hypothesis Testing: Null and Alternative Hypothesis (one sample t test)! More Statistics & R Programming Videos: https://goo.gl/4vDQzT ►► Like to support us? You can Donate (https://bit.ly/2CWxnP2) or Share our videos with your friends! In the second video in Statistics 101 Hypothesis Testing series, we will learn about the null and alternative hypotheses and how they are set up in a hypothesis test in the context of a one-sample t-test. ►Hypothesis testing works by first specifying a Null Hypothesis and an Alternative Hypothesis. The Null hypothesis is generally a statement of “no change” or “nothing interesting happening here”, while the Alternative hypothesis is generally what we are interested in “proving”, or more correctly, what we are interested in “providing evidence for”. Hypothesis tests generally start by assuming the Null hypothesis to be true, and then proceed to work out how likely we would have been to observed what we did in our sample (the sample statistic, or sample mean in this case) if the Null hypothesis were in fact true. This “how likely we were to observe it” is known as a p value. ►The One Sample t Test helps us decide whether or not we believe the sample mean is statistically different from a known or hypothesized population mean. The One Sample t Test is a parametric test. This test is also known as: Single Sample t Test or Student’s t test or when one assumes the population standard deviation is known, it is called the Z test. The test works by calculating a test statistic that measures how compatible the sample statistic (the sample mean in this case) is with the value that would be expected for the sample statistic if the null hypothesis were in fact true (the null hypothesized value). A p value is then calculated. The p value tells us the probability of obtaining a sample statistic as far, or further, from the null hypothesized value, if the null hypothesis were in fact true. The p value helps us decide whether or not we will believe the null hypothesis to be true or not. In this set of tutorials (Statistics 101), you will learn the concept of a null and alternative hypothesis, how a test statistic can be used to measure the compatibility of our data with the null hypothesis, the use of a significance level and p-values or critical regions, conclusions that we can make as well as the errors that may be made when drawing our conclusions. ►► Like to support us? You can Donate (https://bit.ly/2CWxnP2), Money is tight? Share our videos with your friends and let our videos reach more people! Either way Thank You! ►► Watch More: ► Intro to Statistics Course: https://bit.ly/2SQOxDH ►R Tutorials for Data Science https://bit.ly/1A1Pixc ►Getting Started with R (Series 1): https://bit.ly/2PkTneg ►Graphs and Descriptive Statistics in R (Series 2): https://bit.ly/2PkTneg ►Probability distributions in R (Series 3): https://bit.ly/2AT3wpI ►Bivariate analysis in R (Series 4): https://bit.ly/2SXvcRi ►Linear Regression in R (Series 5): https://bit.ly/1iytAtm ►ANOVA Concept and with R https://bit.ly/2zBwjgL Follow MarinStatsLectures Subscribe: https://goo.gl/4vDQzT website: https://statslectures.com Facebook:https://goo.gl/qYQavS Twitter:https://goo.gl/393AQG Instagram: https://goo.gl/fdPiDn Our Team: Content Creator: Mike Marin (B.Sc., MSc.) Senior Instructor at UBC. Producer and Creative Manager: Ladan Hamadani (B.Sc., BA., MPH) These videos are created by #marinstatslectures to support some courses at The University of British Columbia (UBC) (#IntroductoryStatistics and #RVideoTutorials for Health Science Research), although we make all videos available to the everyone everywhere for free. Thanks for watching! Have fun and remember that statistics is almost as beautiful as a unicorn!
Views: 14599 MarinStatsLectures- R Programming & Statistics
Visit http://www.statisticshowto.com for more information on the null hypothesis.
Views: 179537 Stephanie Glen
SKIP AHEAD: 0:39 – Null Hypothesis Definition 1:42 – Alternative Hypothesis Definition 3:12 – Type 1 Error (Type I Error) 4:16 – Type 2 Error (Type II Error) 4:43 – Power and beta 6:33 – p-Value 8:39 – Alpha and statistical significance 14:15 – Statistical hypothesis testing (t-test, ANOVA & Chi Squared) For the text of this video click here http://www.stomponstep1.com/p-value-null-hypothesis-type-1-error-statistical-significance/ For my video on Confidence Intervals click here http://www.stomponstep1.com/confidence-interval-interpretation-95-confidence-interval-90-99/
Views: 425275 Stomp On Step 1
To use data and statistics properly, it's important to understand hypotheses. In particular, it's important to understand the difference between null and research hypotheses. Knowing more about hypotheses as I describe here will help you better understand the concept of null hypothesis significance testing, or the overall topic of statistical significance.
Views: 28221 Ben Baran
How is Null hypothesis different from Alternative Hypothesis? An explanation with a simple example " Effect of fertilizer 'x' on plant growth" (Less than 5 min video) This video include -What is hypothesis? -Definition of Null hypothesis and Alternative Hypothesis. -Summary of Scientific method -Difference between independent and dependant variable in an experiment. For notes: http://www.majordifferences.com/2016/10/5-differences-between-null-and.html
Views: 69414 biologyexams4u
There are two types of hypotheses we need for hypothesis testing: the one we test (the null hypothesis) and the one that use instead if we reject the null hypothesis (the alternative hypothesis). The null hypothesis (H0) states there is no difference between the experimental (sample) mean and the control (population) mean; therefore, any differences between the experimental mean and the control (population) mean are due to chance. The null hypothesis is also a falsifiable hypothesis. Table of Contents: 00:24 - Null Hypothesis 01:36 - Alternative Hypothesis
Views: 7654 Research By Design
This video provides a examples of null and alternative hypotheses in hypothesis testing. Learn how to correctly state the null and alternative hypothesis in statistics.
Views: 5164 Quantitative Specialists
This lesson on inferential statistics shows you how to do the hypothesis testing procedure. From writing out the 2 competing hypotheses to determining if you are rejecting or not rejecting the null hypothesis. http://www.numberbender.com/ Lesson on how to write null and alternative hypotheses in inferential statistics ===================== For more math video updates, subscribe here! https://www.youtube.com/user/TheNumberBender Follow us on Twitter https://twitter.com/number_bender Like us on Facebook https://www.facebook.com/thenumberbender Thank you, Peter
Views: 8349 Numberbender
The lecture builds up on Significance Testing based on previous lectures. We demonstrate hypothesis formulating, setting a alpha level to test the hypothesis against. Single sample test of means are discussed in the lecture alongwith acceptance and rejection regions around the hypothesized means. The lecture demonstrates using an example where we claim a certain hypothesis regarding the mean of the population. Using CLT – central limit theorem properties, we test the claim using sample mean and sample standard deviation. This playlist provides approximately 10 hours of our Analytics Training series. For more information, please visit www.learnanalytics.in . For enquiries drop an email to [email protected] . The training covers basic business statistics concepts and using tools such as SAS, SPSS , Statistica and R using Rattle. The objective of the training series is to prepare the student for a career in Data Analysis and the Analytics Industry in general. Please visit our website for further details. If you wish to subscribe to our full Analytics Training module, please visit http://goo.gl/nIJJHg for our paid Youtube Channel which contains additional hours covering more extensive topics including Linear Regression/Logistic Regression, building and testing predictive models using Logistic / Decision Trees and Ensembling. All videos on our paid channel are available without advertisement interruptions and you can enrol for a 14 day free subscription trial. You pay only if you want to continue. Additionally, you get access to the datasets discussed in the videos and all SAS Codes.
Views: 5036 Learn Analytics
Step 2 in the five steps of hypothesis testing is to create a null and alternative hypothesis. The null hypothesis states that there is no difference between the sample mean and the population mean, so any differences are due to chance. The alternative hypothesis states that the sample mean and the population mean are truly different, so any differences are real and are due to a treatment effect. Alternative hypotheses can be either directional or non-directional. Directional refers to the direction that the dependent variable changes. We establish hypotheses for our baby weight example. Course files & Bear Handout: https://drive.google.com/drive/folders/1n9aCsq5j4dQ6m_sv62ohDI69aol3rW6Q?usp=sharing Table of Contents: 02:12 - Step 2: Null and Alternative Hypothesis 02:23 - Step 2: Null and Alternative Hypothesis 04:24 - Step 2: Null and Alternative Hypothesis 05:11 -
Views: 1664 Research By Design
This is just a few minutes of a complete course. Get full lessons & more subjects at: http://www.MathTutorDVD.com.
Views: 2944 mathtutordvd
📚📚📚📚📚📚📚📚 GOOD NEWS FOR COMPUTER ENGINEERS INTRODUCING 5 MINUTES ENGINEERING 🎓🎓🎓🎓🎓🎓🎓🎓 SUBJECT :- Artificial Intelligence(AI) Database Management System(DBMS) Software Modeling and Designing(SMD) Software Engineering and Project Planning(SEPM) Data mining and Warehouse(DMW) Data analytics(DA) Mobile Communication(MC) Computer networks(CN) High performance Computing(HPC) Operating system System programming (SPOS) Web technology(WT) Internet of things(IOT) Design and analysis of algorithm(DAA) 💡💡💡💡💡💡💡💡 EACH AND EVERY TOPIC OF EACH AND EVERY SUBJECT (MENTIONED ABOVE) IN COMPUTER ENGINEERING LIFE IS EXPLAINED IN JUST 5 MINUTES. 💡💡💡💡💡💡💡💡 THE EASIEST EXPLANATION EVER ON EVERY ENGINEERING SUBJECT IN JUST 5 MINUTES. 🙏🙏🙏🙏🙏🙏🙏🙏 YOU JUST NEED TO DO 3 MAGICAL THINGS LIKE SHARE & SUBSCRIBE TO MY YOUTUBE CHANNEL 5 MINUTES ENGINEERING 📚📚📚📚📚📚📚📚
Views: 5207 5 Minutes Engineering
I have made a new and improved version of this video to correct a mistake. To be take to the new video please click here https://www.youtube.com/watch?v=YSwmpAmLV2s
Views: 90483 Stomp On Step 1
Excel file: https://dl.dropboxusercontent.com/u/561402/TTEST.xls In this video Paul Andersen explains how to run the student's t-test on a set of data. He starts by explaining conceptually how a t-value can be used to determine the statistical difference between two samples. He then shows you how to use a t-test to test the null hypothesis. He finally gives you a separate data set that can be used to practice running the test. Do you speak another language? Help me translate my videos: http://www.bozemanscience.com/translations/ Music Attribution Intro Title: I4dsong_loop_main.wav Artist: CosmicD Link to sound: http://www.freesound.org/people/CosmicD/sounds/72556/ Creative Commons Atribution License Outro Title: String Theory Artist: Herman Jolly http://sunsetvalley.bandcamp.com/track/string-theory All of the images are licensed under creative commons and public domain licensing: 184.108.40.206.2. Critical Values of the Student’s-t Distribution. (n.d.). Retrieved April 12, 2016, from http://www.itl.nist.gov/div898/handbook/eda/section3/eda3672.htm File:Hordeum-barley.jpg - Wikimedia Commons. (n.d.). Retrieved April 11, 2016, from https://commons.wikimedia.org/wiki/File:Hordeum-barley.jpg Keinänen, S. (2005). English: Guinness for strenght. Retrieved from https://commons.wikimedia.org/wiki/File:Guinness.jpg Kirton, L. (2007). English: Footpath through barley field. A well defined and well used footpath through the fields at Nuthall. Retrieved from https://commons.wikimedia.org/wiki/File:Footpath_through_barley_field_-_geograph.org.uk_-_451384.jpg pl.wikipedia, U. W. on. ([object HTMLTableCellElement]). English: William Sealy Gosset, known as “Student”, British statistician. Picture taken in 1908. Retrieved from https://commons.wikimedia.org/wiki/File:William_Sealy_Gosset.jpg The T-Test. (n.d.). Retrieved April 12, 2016, from http://www.socialresearchmethods.net/kb/stat_t.php
Views: 494713 Bozeman Science