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Hypothesis test for difference of means video Khan Academy

Hypothesis testing two meansHypothesis Test for Difference of Means. Prepare with these 2 lessons on Two-sample inference for the difference between groups. "probability of the difference of the samples means being 1.91 or more assuming the difference of the populations means is 0" this is what Sal does here, except that he only tries to prove. Contents Basics Introduction Data analysis steps Kinds of biological variables Probability Hypothesis testing Confounding variables Tests for nominal variables Exact test of goodness-of-fit Power analysis Chi-square test of goodness-of-fit –test Wilcoxon signed-rank test Tests for multiple measurement variables Linear regression and correlation Spearman rank correlation Polynomial regression Analysis of covariance Multiple regression Simple logistic regression Multiple logistic regression Multiple tests Multiple comparisons Meta-analysis Miscellany Using spreadsheets for statistics Displaying results in graphs Displaying results in tables Introduction to SAS Choosing the right test value, which is the probability of obtaining the observed results, or something more extreme, if the null hypothesis were true. If the observed results are unlikely under the null hypothesis, your reject the null hypothesis. Alternatives to this "frequentist" approach to statistics include Bayesian statistics and estimation of effect sizes and confidence intervals. The technique used by the vast majority of biologists, and the technique that most of this handbook describes, is sometimes called "frequentist" or "classical" statistics. It involves testing a null hypothesis by comparing the data you observe in your experiment with the predictions of a null hypothesis. You estimate what the probability would be of obtaining the observed results, or something more extreme, if the null hypothesis were true. Next


Conducting hypothesis tests for the difference between two means.

Hypothesis testing two meansThis tutorial covers the steps for conducting hypothesis tests for the difference between two means in StatCrunch. To begin, load the Asking prices for 4-bedroom homes in Bryan-College Station TX data set, which will be used throughout this tutorial. The data set was collected in order to compare four-bedroom homes listed. (7) Conclusion From these data, it can be concluded that the population means are not equal. A 95% confidence interval would give the same conclusion. Sampling from normally distributed populations with unknown variances wish to know if we may conclude, at the 95% confidence level, that smokers, in general, have greater lung damage than do non-smokers. (1) Data Smokers: = 17.5 = 16 = 4.4752 Non-Smokers: = 12.4 = 9 = 4.8492 = .05 Calculation of Pooled Variance: (2) Assumptions (4) Test statistic (a) Distribution of test statistic If the assumptions are met and is true, the test statistic is distributed as Student's t distribution with 23 degrees of freedom. (b) Decision rule data were obtained in a study comparing persons with disabilities with persons without disabilities. A scale known as the Barriers to Health Promotion Activities for Disabled Persons (BHADP) Scale gave the data. Next


Hypothesis test for difference of means Probability and Statistics.

Hypothesis testing two meansNov 4, 2010. Hypothesis Test for Difference of Means Watch the next lesson https// This Hypothesis Testing Calculator determines whether an alternative hypothesis is true or not. Based on whether it is true or not determines whether we accept or reject the hypothesis. We accept true hypotheses and reject false hypotheses. The null hypothesis is the hypothesis that is claimed and that we will test against. The alternative hypothesis is the hypothesis that we believe it actually is. For example, let's say that a company claims it only receives 20 consumer complaints on average a year. However, we believe that most likely it receives much more. In this case, the null hypothesis is the claimed hypothesis by the company, that the average complaints is 20 (μ=20). Next


TWO-SAMPLE TEST OF A HYPOTHESIS - Elon University

Hypothesis testing two meansAug 21, 2003. Two-sample hypothesis testing is statistical analysis designed to test if there is a difference between two means from two different populations. For example, a two-sample hypothesis could be used to test if there is a difference in the mean salary between male and female doctors in the New York City area. Based on Theorem 2 of Chi-square Distribution and its corollaries, we can use the chi-square distribution to test the variance of a distribution. Example 1: A company produces metal pipes of a standard length. Twenty years ago it tested its production quality and found that the lengths of the pipes produced were normally distributed with a standard deviation of 1.1 cm. They want to test whether they are still meeting this level of quality by testing a random sample of 30 pipes, and finding the 95% confidence interval around , and so the approach used in Confidence Intervals for Sampling Distributions and Confidence Interval for t-test needs to be modified somewhat, in that we need to calculate the lower and upper values of the confidence interval based on different critical values of the distribution: Upper limit = 0.042*CHIINV(.025, 29) = 0.042 ∙ 45.72 = 1.91 Lower limit = 0.042*CHIINV(.975, 29) = 0.042 ∙ 16.05 = 0.67 And so the confidence interval is (0.67, 1.91). We see that the variance of (1.1) = 1.21 is in this range, but the sample is too small to get much precision. Next


Hypothesis Testing - Two Means - Large Independent Samples.

Hypothesis testing two meansFeb 3, 2016. This is just a few minutes of a complete course. Get full lessons & more subjects at In this lesson the student will gain practice solving problems involving hypothesis testing in statistics. In these problems we perform the hypothesis test between two population means with. You performed a one-sample bootstrap hypothesis test, which is impossible to do with permutation. Testing the hypothesis that two samples have the same distribution may be done with a bootstrap test, but a permutation test is preferred because it is more accurate (exact, in fact). But therein lies the limit of a permutation test; it is not very versatile. We now want to test the hypothesis that Frog A and Frog B have the same mean impact force, but not necessarily the same distribution. To do the two-sample bootstrap test, we shift arrays to have the same mean, since we are simulating the hypothesis that their means are, in fact, equal. We then draw bootstrap samples out of the shifted arrays and compute the difference in means. This constitutes a bootstrap replicate, and we generate many of them. The p-value is the fraction of replicates with a difference in means greater than or equal to what was observed. Next


Hypothesis Testing of the Difference Between Two Population Means

Hypothesis testing two meansThe file follows this text very closely and readers are encouraged to consult the text for further information. B Hypothesis testing of the difference between two population means. This is a two sample z test which is used to determine if two population means are equal or unequal. There are three possibilities for formulating. This approach consists of four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. Every hypothesis test requires the analyst to state a null hypothesis and an alternative hypothesis. The hypotheses are stated in such a way that they are mutually exclusive. That is, if one is true, the other must be false; and vice versa. The table below shows three sets of null and alternative hypotheses. Next


Testing Differences between Two Means

Hypothesis testing two meansCritical value comes from standard normal z distribution. Use one- or two-tailed test. Conservatively, choose the two-tailed test. Values are also available at bottom of. The Step-by-Step Approach. Step 1 State hypotheses. Two-tailed One-tailed 0. 1. 2. 0. 1. 2. 0. 1. 2. H = H # or H $ 1. 1. 2. 1. 1. 2. 1. 1. 2. H. This is the first of three modules that will addresses the second area of statistical inference, which is hypothesis testing, in which a specific statement or hypothesis is generated about a population parameter, and sample statistics are used to assess the likelihood that the hypothesis is true. The hypothesis is based on available information and the investigator's belief about the population parameters. The process of hypothesis testing involves setting up two competing hypotheses, the null hypothesis and the alternate hypothesis. One selects a random sample (or multiple samples when there are more comparison groups), computes summary statistics and then assesses the likelihood that the sample data support the research or alternative hypothesis. Similar to estimation, the process of hypothesis testing is based on probability theory and the Central Limit Theorem. This module will focus on hypothesis testing for means and proportions. The next two modules in this series will address analysis of variance and chi-squared tests. In estimation we focused explicitly on techniques for one and two samples and discussed estimation for a specific parameter (e.g., the mean or proportion of a population), for differences (e.g., difference in means, the risk difference) and ratios (e.g., the relative risk and odds ratio). Next


Hypothesis Test Difference in Means - Stat Trek

Hypothesis testing two meansHow to conduct a hypothesis test to determine whether the difference between two mean scores is significant. Includes examples for one- and two-tailed tests. Hypothesis testing is an essential procedure in statistics. A hypothesis test evaluates two mutually exclusive statements about a population to determine which statement is best supported by the sample data. When we say that a finding is statistically significant, it’s thanks to a hypothesis test. How do these tests really work and what does statistical significance actually mean? In this series of three posts, I’ll help you intuitively understand how hypothesis tests work by focusing on concepts and graphs rather than equations and numbers. After all, a key reason to use statistical software like Minitab is so you don’t get bogged down in the calculations and can instead focus on understanding your results. To kick things off in this post, I highlight the rationale for using hypothesis tests with an example. An economist wants to determine whether the monthly energy cost for families has changed from the previous year, when the mean cost per month was $260. Next


Testing Differences Between Means - OnlineStatBook

Hypothesis testing two meansState the assumptions for testing the difference between two means; Estimate the population variance assuming homogeneity of variance; Compute the standard error of the difference between means; Compute t and p for. The hypothesized value is the null hypothesis that the difference between population means is 0. If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.and *.are unblocked. Next


T-Test with TI-83 Calculator

Hypothesis testing two meansExample Two samples were taken, one from each of two populations. Use the TI-83 calculator to test the hypothesis that the two population means are equal with a level of significance of a = 2%. Solution For the two samples, we have the following summary data. Confidence intervals and Hypothesis tests are very important tools in the Business Statistics toolbox. A mastery over these topics will help enhance your business decision making and allow you to understand and measure the extent of ‘risk’ or ‘uncertainty’ in various business processes. This is the third course in the specialization "Business Statistics and Analysis" and the course advances your knowledge about Business Statistics by introducing you to Confidence Intervals and Hypothesis Testing. We first conceptually understand these tools and their business application. We then introduce various calculations to constructing confidence intervals and to conduct different kinds of Hypothesis Tests. To successfully complete course assignments, students must have access to a Windows version of Microsoft Excel 2010 or later. Please note that earlier versions of Microsoft Excel (2007 and earlier) will not be compatible to some Excel functions covered in this course. WEEK 1 Module 1: Confidence Interval - Introduction In this module you will get to conceptually understand what a confidence interval is and how is its constructed. We will introduce the various building blocks for the confidence interval such as the t-distribution, the t-statistic, the z-statistic and their various excel formulas. Next


Comparison of Two Means

Hypothesis testing two meansGiven samples from two normal populations of size n1 and n2 with unknown means and and known standard deviations and, the test statistic comparing the means is known as the two-sample z statistic. which has the standard normal distribution N0,1. The null hypothesis always assumes that the means are equal. In 2005, Larry Summers, then President of Harvard, gave a speech at the NBER Conference on Diversifying the Science and Engineering Workforce. In that speech, he made some very controversial remarks regarding differences in the genders. In particular, It does appear that on many, many different human attributes-height, weight, propensity for criminality, overall IQ, mathematical ability, scientific ability-there is relatively clear evidence that whatever the difference in means-which can be debated-there is a difference in the standard deviation, and variability of a male and a female population. Suppose we wanted to do a comparison between the genders. In Section 11.2, we looked at comparing two means with matched-pairs data - dependent samples. What if there isn't a relationship between the two samples? We certainly can't pair them up then, and find the Note: There is no exact method for comparing two means with unequal populations, but this statistic is a close approximation. It is known as Welch's approximate t, in honor of English statistician Bernard Lewis Welch (1911-1989). Next


Comparing two independent means hypothesis testing - Decision.

Hypothesis testing two meansJul 8, 2016. Video created by Duke University for the course "Bayesian Statistics". In this module, we will discuss Bayesian decision making, hypothesis testing, and Bayesian testing. By the end of this week, you will be able to make optimal decisions based. The amount of a certain trace element in blood is known to vary with a standard deviation of 14.1 ppm (parts per million) for male blood donors and 9.5 ppm for female donors. Random samples of 75 male and 50 female donors yield concentration means of 28 and 33 ppm, respectively. What is the likelihood that the population means of concentrations of the element are the same for men and women? Null hypothesis: H The computed z‐value is negative because the (larger) mean for females was subtracted from the (smaller) mean for males. But because the hypothesized difference between the populations is 0, the order of the samples in this computation is arbitrary— could just as well have been the female sample mean and the male sample mean, in which case z would be 2.37 instead of –2.37. An extreme z‐score in either tail of the distribution (plus or minus) will lead to rejection of the null hypothesis of no difference. The area of the standard normal curve corresponding to a z‐score of –2.37 is 0.0089. Because this test is two‐tailed, that figure is doubled to yield a probability of 0.0178 that the population means are the same. Next


Hypothesis Tests for One or Two Means - Milefoot

Hypothesis testing two meansHypothesis Tests for One or Two Means. When testing a claim about the value of a population mean, the test statistic will depend on whether the population standard deviation is known or unknown. This situation is identical to finding a confidence interval for a mean, and is resolved in exactly the same way. This is the first of three modules that will addresses the second area of statistical inference, which is hypothesis testing, in which a specific statement or hypothesis is generated about a population parameter, and sample statistics are used to assess the likelihood that the hypothesis is true. The hypothesis is based on available information and the investigator's belief about the population parameters. The process of hypothesis testing involves setting up two competing hypotheses, the null hypothesis and the alternate hypothesis. One selects a random sample (or multiple samples when there are more comparison groups), computes summary statistics and then assesses the likelihood that the sample data support the research or alternative hypothesis. Similar to estimation, the process of hypothesis testing is based on probability theory and the Central Limit Theorem. Next


Two-Sample t-Test for Equal Means

Hypothesis testing two meansTest Statistic where N1 and N2 are the sample sizes, and are the sample means, and and are the sample variances. If equal variances are assumed, then the formula reduces to where. Significance Level α. Critical Region Reject the null hypothesis that the two means are equal if. T t1-α/2,ν. where t1-α/2,ν is the critical. The amount of a certain trace element in blood is known to vary with a standard deviation of 14.1 ppm (parts per million) for male blood donors and 9.5 ppm for female donors. Random samples of 75 male and 50 female donors yield concentration means of 28 and 33 ppm, respectively. What is the likelihood that the population means of concentrations of the element are the same for men and women? Null hypothesis: H The computed z‐value is negative because the (larger) mean for females was subtracted from the (smaller) mean for males. But because the hypothesized difference between the populations is 0, the order of the samples in this computation is arbitrary— could just as well have been the female sample mean and the male sample mean, in which case z would be 2.37 instead of –2.37. Next


Comparing two large sample means

Hypothesis testing two meansQuestion Type Hypothesis test; Data Structure Two sample means, independent samples; Sample Size Large; Test statistic Two sample Z-test. Let $\mu_M$ and $\mu_F$ be the true average weight loss for Magic Merv's and the ``Fat, What Fat?'' diets, respectively. Then, we are asked to test the hypotheses. This tutorial covers the steps for conducting hypothesis tests for the difference between two means in Stat Crunch. To begin, load the Asking prices for 4-bedroom homes in Bryan-College Station TX data set, which will be used throughout this tutorial. The data set was collected in order to compare four-bedroom homes listed for sale in the two adjoining cities of Bryan, Texas, and College Station, Texas. Using a real estate web site, fifteen homes were randomly selected from four-bedroom homes listed for sale in Bryan, Texas, and fifteen homes were randomly selected from four-bedroom homes listed for sale in College Station, Texas. The column lists the city where the home is located. This tutorial will cover using two-sample T methods for this raw data set with individual measurements on each home. A very similar approach can be used for two-sample Z methods that are appropriate for situations with larger sample sizes and/or known standard deviations. To compute two-sample results using the sample mean, sample standard deviation and sample size for two samples, see Conducting hypothesis tests for the difference between two means with summary data. Next


Hypothesis Testing Two sample mean - Andrews University

Hypothesis testing two meansHypothesis Testing Two sample means. Lesson Overview. Unmatched independent Two-sample t Test; Effect Size; Testing Variance Homogeneity; Matched dependent Pair Test; HT two-sample, other statistics; Homework. Often one wants to compare two treatments or populations and determine if there is a difference. So far in our course, we have only discussed measurements taken in one variable for each sampling unit. In this lesson, we are going to talk about measurements taken in two variables for each sampling unit. In this lesson, we are going to talk about the very practical problem of situations where two measurements are being compared. To begin, just as we did in the case for one-proportion or one-mean, one has to first decide whether the problem you are investigating requires the analysis of categorical or quantitative data. Next, one has to determine if the samples are independent samples or dependent samples in order to choose between a 2-sample test and the paired test. We will start with comparing two independent population proportions, move to comparing two independent population means, from there to paired population means, and ending with the comparison of two independent population variances. The latter can help us determine in the analysis of two independent population means whether to use the equal variances 2-sample -test. Next


Introducing the Difference-In-Means Hypothesis Test - Coursera

Hypothesis testing two meansJan 9, 2017. You get to understand the logic behind hypothesis tests. The four steps for conducting a hypothesis test are introduced and you get to apply them for hypothesis tests for a population mean as well as population proportion. You will understand the difference between single tail hypothesis tests and two tail. The investment profession stands at an inflection point, and we can’t rely on old models and maxims. CFA Institute provides in-depth insights on the world of today in order to push the industry into the future. When you need to see more, know more, do more: CFA Institute is there. Next


Hypothesis Test for a Difference Between Two Means unpaired.

Hypothesis testing two meansApr 15, 2012. This is an example of a hypothesis test bwteen two sample means. This is an unpaired test. Hypothesis testing and estimation are used to reach conclusions about a population by examining a sample of that population. Hypothesis testing is widely used in medicine, dentistry, health care, biology and other fields as a means to draw conclusions about the nature of populations. Hypothesis testing is to provide information in helping to make decisions. The administrative decision usually depends a test between two hypotheses. Definitions Hypothesis: A hypothesis is a statement about one or more populations. There are research hypotheses and statistical hypotheses. Research hypotheses: A research hypothesis is the supposition or conjecture that motivates the research. It may be proposed after numerous repeated observation. Research hypotheses lead directly to statistical hypotheses. Next


Hypothesis testing two meansHypothesis Testing, Statistical Significance, and Independent t Tests Hypothesis Testing and Statistical Significance When a hypothesis is tested by collecting data. These values are obtained from the inverse of the cumulative distribution function of the standard normal distribution. This is called the An automobile company is looking for fuel additives that might increase gas mileage. For example, when we look for the probability, say, that $Z where $\mu$ is the true mean and $\mu_0$ is the current accepted population mean. When $n$ is large enough and the null hypothesis is true the sample means often follow a normal distribution with mean $\mu_0$ and standard deviation $\frac$. Without additives, their cars are known to average $25$ mpg (miles per gallons) with a standard deviation of $2.4$ mpg on a road trip from London to Edinburgh. The company now asks whether a particular new additive increases this value. In a study, thirty cars are sent on a road trip from London to Edinburgh. Suppose it turns out that the thirty cars averaged $\overline=25.5$ mpg with the additive. Can we conclude from this result that the additive is effective? We are asked to show if the new additive increases the mean miles per gallon. We start with the assumption the normal distribution is still valid. Next


Lesson 39 Tests of the Equality of Two Means STAT 414 / 415

Hypothesis testing two meansPrinter-friendly version. Introduction. In this lesson, we'll continue our investigation of hypothesis testing. In this case, we'll focus our attention on a hypothesis test for the difference in two population means μ1−μ2 for two situations a hypothesis test based on the t-distribution, known as the pooled two-sample t-test, for μ1−μ2. We consider here the population of platypus gene GC contents (full download available here). This population has a mean and standard deviation : We will describe four sampling distributions of the mean from this population distribution. Each sampling distribution contains N sample means, computed from N random samples drawn from the population. You can download each here: The following examples all utilize the same data set, for explanatory purposes. In general, do not perform multiple tests on the same data, until we have learned how to do so safely later this semester. Length, mu = 6.15) One Sample t-test data: virginica$Sepal. Length t = 4.8706, df = 49, p-value = 1.204e-05 alternative hypothesis: true mean is not equal to 6.15 95 percent confidence interval: 6.407285 6.768715 sample estimates: mean of x 6.588 Our test statistic is 4.87 with 49 degrees of freedom. We therefore reject the null hypothesis and conclude that there is evidence that virginica sepal lengths differ from 6.15. We can further conclude that virginica sepal lengths are larger than 6.15 (sample mean = 6.59). We have a 95% confidence interval of [6.41, 6.76], meaning there is a 95% chance that the true population mean falls in this range. Next


Hypothesis testing two population means - YouTube

Hypothesis testing two meansMay 14, 2012. This video introduces hypothesis tests of two population means, sometimes called two-sample tests. I hope you find it useful! This lesson describes some refinements to the hypothesis testing approach that was introduced in the previous lesson. The truth of the matter is that the previous lesson was somewhat oversimplified in order to focus on the concept and general steps in the hypothesis testing procedure. With that background, we can now get into some of the finer points of hypothesis testing. This lesson describes some refinements to the hypothesis testing approach that was introduced in the previous lesson. The truth of the matter is that the previous lesson was somewhat oversimplified in order to focus on the concept and general steps in the hypothesis testing procedure. With that background, we can now get into some of the finer points of hypothesis testing. The "two sample case" is a special case in which the is examined. This sounds like what we did in the last lesson, but we actually looked at the difference between an observed or sample group mean and a control group mean, which was treated as if it were a population mean (rather than an observed or sample mean). Next


Difference Between Means Hypothesis Testing of the. - LTCC Online

Hypothesis testing two meansDifference Between Means. Hypothesis Testing of the Difference Between Two Means. Do employees perform better at work with music playing. The music was turned on during the working hours of a business with 45 employees. There productivity level averaged 5.2 with a standard deviation of 2.4. On a different day the. This tutorial covers the steps for conducting hypothesis tests for the difference between two means in Stat Crunch. To begin, load the Asking prices for 4-bedroom homes in Bryan-College Station TX data set, which will be used throughout this tutorial. The data set was collected in order to compare four-bedroom homes listed for sale in the two adjoining cities of Bryan, Texas, and College Station, Texas. Using a real estate web site, fifteen homes were randomly selected from four-bedroom homes listed for sale in Bryan, Texas, and fifteen homes were randomly selected from four-bedroom homes listed for sale in College Station, Texas. The column lists the city where the home is located. Next


Lesson 8 - Comparing Two Population Means, Two Proportions or.

Hypothesis testing two meansYou will find that much of what we discuss here will be an extension to our previous lessons on confidence intervals and hypothesis testing for one-proportion and one-mean. We will want to check necessary conditions in order to use Z-methods for comparing two proportions or to use t-methods for comparing two means. To compare the difference between two means, two averages, two proportions or two counted numbers. The means are from two independent sample or from two groups in the same sample. A number of additional statistics for comparing two groups are further presented. Next


Hypothesis tests to compare means of two populations - UT Dallas

Hypothesis testing two meansWhere $\mu_1$ represents the population mean salary of all male financial analysts and $\mu_2$ represents the population mean salary of all female financial analysts. This problem is stated as a two-sided hypothesis so that we can detect an increase as well as a decrease in female salaries compared to male salaries. The main purpose of statistics is to test a hypothesis. For example, you might run an experiment and find that a certain drug is effective at treating headaches. But if you can’t repeat that experiment, no one will take your results seriously. A good example of this was the cold fusion discovery, which petered into obscurity because no one was able to duplicate the results. Contents (Click to skip to the section): as long as you can put it to the test. If you are going to propose a hypothesis, it’s customary to write a statement. Your statement will look like this: “If I…(do this to an independent variable)…(this will happen to the dependent variable).” For example: Hypothesis testing in statistics is a way for you to test the results of a survey or experiment to see if you have meaningful results. You’re basically testing whether your results are valid by figuring out the odds that your results have happened by chance. Next


Student's t-test Comparison of two means

Hypothesis testing two meansOne of these tests is used for the comparison of two means, which is commonly applied to many cases. Typical examples are Example. The null hypothesis generally states that "Any differences, discrepancies, or suspiciously outlying results are purely due to random and not systematic errors". The alternative hypothesis. The One Sample t Test determines whether the sample mean is statistically different from a known or hypothesized population mean. This test is also known as: Note: The One Sample t Test can only compare a single sample mean to a specified constant. It can not compare sample means between two or more groups. If you wish to compare the means of multiple groups to each other, you will likely want to run an Independent Samples t Test (to compare the means of two groups) or a One-Way ANOVA (to compare the means of two or more groups). The test statistic for a One Sample t Test is denoted t, which is calculated using the following formula: $$ t = \frac $$ where $$ s_ = \frac $$ where \(\mu\) = Proposed constant for the population mean \(\bar\) = Sample mean \(n\) = Sample size (i.e., number of observations) \(s\) = Sample standard deviation \(s_\) = Estimated standard error of the mean ( Your data should include one continuous, numeric variable (represented in a column) that will be used in the analysis. The variable's measurement level should be defined as Scale in the Variable View window. The One-Sample T Test window opens where you will specify the variables to be used in the analysis. All of the variables in your dataset appear in the list on the left side. Move variables to the Test Variable(s) area by selecting them in the list and clicking the arrow button. Test Variable(s): The variable whose mean will be compared to the hypothesized population mean (i.e., Test Value). Next