hypothesis testing applet

Last revised: January 28, 2013

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Tutorial: Hypothesis Testing

Sadly, browsers no longer support the interactive java applet that is featured in this tutorial., introduction to hypothesis testing.

Overview : Statistical hypothesis testing is a method of making decisions about a population based on sample data. We can compute how likely it is to find specific sample data if the sample was drawn randomly from the hypothesized population. For example, we can determine if graduates of a training program on average obtain higher test scores than individuals who did not take this training program.

What do I need to know? To make best use of this exercise, you should know how the sampling distribution of the mean is related to sample size and the population variance. It would be helpful to have completed the WISE tutorials on the Sampling Distribution and Central Limit Theorem . A quick review of these topics and the normal distribution can be found at the bottom of this page.

What do I need? You will need a calculator to answer some questions. If you will need to submit your responses to your instructor, download the Tutorial Worksheet to use as you go through the tutorial.

Instructions: You will be asked questions and you will be given feedback regarding your answers. We provide detailed explanations, but you should try to answer the questions on your own before consulting our solutions. You will learn much more by doing the exercises yourself than if you merely read them and the answers.

At the end of the tutorial, you will be able to test your knowledge with our online quiz on hypothesis testing or gain further practice on a set of questions similar to those in the tutorial.

Optional review material:

• Review Sampling Distribution of the Mean
• Review Central Limit Theorem
• Review z -scores and the Normal Distribution

Let’s Get Started!

Suggested format for citing this tutorial: Berger, D. E. & Saw, A. T. (2008). WISE Hypothesis Testing Tutorial. Retrieved [date] from https://wise.cgu.edu .

We would like to thank the following individuals for their work on an older version of a Hypothesis Testing tutorial which this version is based on: Chris Aberson, Michael Healy, Victoria Romero, and Diana Kyle.

Questions, comments, difficulties? See our technical support page or contact us: [email protected] .

Conceptual Learning with Interactive Applets

Interactive applets for undergraduate mathematics and statistics

Conceptual Learning with Interactive Applets is a project to build high-quality web-based applets and supporting resources for enhancing conceptual understanding in undergraduate mathematics and statistics. Our applets are built using GeoGebra .

The project is based in the University of Melbourne , School of Mathematics and Statistics , and funded by a University of Melbourne Learning & Teaching Initiatives grant.

Select a subject to view applets for that subject, or browse the full collection below.

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This applet demonstrates the Gram-Schmidt algorithm performed in $\mathbb R^3$. The Gram-Schmidt algorithm converts a basis of an inner product space into an orthonormal basis. It does this by building up the orthonormal basis one vector at a time. For each vector in turn, we remove any component that is parallel to the vectors which […]

This applet shows the geometric effect of a linear transformation $T: \mathbb R^2 \to \mathbb R^2$. You can type a matrix $M$ on the right hand side of the applet, and then click Play to see how the vertices of a triangle are transformed when multiplying by $M$. Other resources: Geogebratube page for this applet

This applet shows the geometric effect of a linear transformation $T$ in $\mathbb R^3$. You can type a 3×3 matrix $M$ on the right hand side of the applet, and then click Play to see how the vertices of a cube are transformed when multiplying by $M$. Can you see if the corresponding transformations are […]

This applet helps visualise the surface generated by cylindrical coordinates using r,θ and z. Click and drag on the sliders on the left to adjust the ranges for r,θ and z. Geogebratube page for this applet

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This applet shows a line in R3 and the vector form of its equation. 

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This applet illustrates the partitioning of variability into explained and unexplained variability, in the context of ANOVA.

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Repeatedly sample from a bivariate population, and construct a histogram of sample regression line slope.

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Learning Materials Business Studies Combined Science Computer Science Engineering English Literature Environmental Science Human Geography Macroeconomics Microeconomics Chapter 10: Problem 31 Load the hypothesis tests for a mean applet. (a) Set the shape to right skewed, the mean to \(50,\) and the standard deviation to \(10 .\) Obtain 1000 simple random samples of size \(n=8\) from this population, and test whether the mean is different from \(50 .\) How many of the samples led to a rejection of the null hypothesis if \(\alpha=0.05 ?\) How many would we expect to lead to a rejection of the null hypothesis if \(\alpha=0.05 ?\) What might account for any discrepancies? (b) Set the shape to right skewed, the mean to \(50,\) and the standard deviation to \(10 .\) Obtain 1000 simple random samples of size \(n=40\) from this population, and test whether the mean is different from \(50 .\) How many of the samples led to a rejection of the null hypothesis if \(\alpha=0.05 ?\) How many would we expect to lead to a rejection of the null hypothesis if \(\alpha=0.05 ?\) Short answer, step by step solution, - configure the applet, - generate samples for part (a), - perform hypothesis test for part (a), - calculate expected rejections for part (a), - analyze discrepancies for part (a), - generate samples for part (b), - perform hypothesis test for part (b), - count rejections for part (b), - calculate expected rejections for part (b), - analyze discrepancies for part (b), key concepts. These are the key concepts you need to understand to accurately answer the question. mean hypothesis test Sample size effect. Smaller sample size (n=8): A small sample means there's more variability in the sample mean. Therefore, you might get more extreme values just by chance, which can lead to more rejections of the null hypothesis than expected. Larger sample size (n=40): With larger samples, the sample mean is likely to be closer to the true population mean (this is due to the Central Limit Theorem). Consequently, the results become more predictable and might show fewer rejections of the null hypothesis due to random fluctuations. significance level α Set α = 0.05: This means we're willing to accept a 5% chance that our significant results are due to random variation (`false positives`), rather than a real effect. Expected rejections: When we tested our 1000 samples, we expected around 5% (or 50 samples) to show significance purely by chance. Comparing results: By comparing the actual number of significant results to our expected 5% (50 samples), we can judge whether our observations are in line with expectations or if other factors (like sample size variability) might be influencing the outcome. One App. One Place for Learning. All the tools & learning materials you need for study success - in one app. Most popular questions from this chapter SAT Exam Scores A school administrator believes that students whose first language learned is not English score worse on the verbal portion of the SAT exam than students whose first language is English. The mean SAT verbal score of students whose first language is English is 515 on the basis of data obtained from the College Board. Suppose a simple random sample of 20 students whose first language learned was not English results in a sample mean SAT verbal score of \(458 .\) SAT verbal scores are normally distributed with a population standard deviation of \(112 .\) (a) Why is it necessary for SAT verbal scores to be normally distributed to test the hypotheses using the methods of this section? (b) Use the classical approach or the \(P\) -value approach at the \(\alpha=0.10\) level of significance to determine if there is evidence to support the administrator's belief. To test \(H_{0}: \mu=105\) versus \(H_{1}: \mu \neq 105,\) a simple random sample of size \(n=35\) is obtained. (a) Does the population have to be normally distributed to test this hypothesis by using the methods presented in this section? (b) If \(\bar{x}=101.9\) and \(s=5.9,\) compute the test statistic. (c) Draw a \(t\) -distribution with the area that represents the \(P\) -value shaded. (d) Determine and interpret the \(P\) -value. (e) If the researcher decides to test this hypothesis at the \(\alpha=0.01\) level of significance, will the researcher reject the null hypothesis? Why? To test \(H_{0}: \mu=20\) versus \(H_{1}: \mu<20,\) a simple random sample of size \(n=18\) is obtained from a population that is known to be normally distributed. (a) If \(\bar{x}=18.3\) and \(s=4.3,\) compute the test statistic. (b) Draw a \(t\) -distribution with the area that represents the \(P\) -value shaded. (c) Approximate and interpret the \(P\) -value. (d) If the researcher decides to test this hypothesis at the \(\alpha=0.05\) level of significance, will the researcher reject the null hypothesis? Why? The mean yield per acre of soybeans on farms in the United States in 2003 was 33.5 bushels, according to data obtained from the U.S. Department of Agriculture. A farmer in Iowa claimed the yield was higher than the reported mean. He randomly sampled 35 acres on his farm and determined the mean yield to be 37.1 bushels, with a standard deviation of 2.5 bushels. He computed the \(P\) -value to be less than 0.0001 and concluded that the U.S. Department of Agriculture was wrong. Why should his conclusions be looked on with skepticism? According to the Insurance Information Institute, the mean expenditure for auto insurance in the United States was \(\$ 774\) for \(2002 .\) An insurance salesman obtains a random sample of 35 auto insurance policies and determines the mean expenditure to be \(\$ 735\) with a standard deviation of \(\$ 48.31 .\) Is there enough evidence to conclude that the mean expenditure for auto insurance is different from the 2002 amount at the \(\alpha=0.01\) level of significance? Recommended explanations on Math Textbooks Discrete mathematics, theoretical and mathematical physics, logic and functions. What do you think about this solution? We value your feedback to improve our textbook solutions. Study anywhere. Anytime. Across all devices. Privacy overview. Rossman/Chance Applet Collection Updated 2021 applets.   - categorical - quantitative - quantitative (click here for help on running java on , )     -intervals for different population shapes     Probability Probability Calculator Statistical Inference    (multiple groups)   (multiple groups)    Multiple Variables (js) (js) (js) (js) (js) Click to access old applets page Teachers: Click to set up memory quiz for your class 416 IMAGES Hypothesis testing Hypothesis testing using the binomial distribution (2.05a) SOLVED:Use the applet Hypothesis Testing (for Proportions) (refer to Use the applet Hypothesis Test for a Mean to investigate the Use the applet Hypothesis Test for a Mean to investigate the WISE Applets COMMENTS Hypothesis tests for a mean The hypothesis test is based on the T statistic. The resulting statistic from the test drops into the plot. Red values represent tests where the null hypothesis is rejected at the specified level of significance. The default significance level of 0.05 used for the tests can be changed by adjusting the Level input within the applet. Hypothesis tests for a proportion The hypothesis test is based on the Z statistic. The resulting statistic from the test drops into the plot. Red values are tests where the null hypothesis is rejected at the specified level of significance. Change the default significance level (set at 0.05) by adjusting the Level in the applet. 5 tests and 1000 tests add the hypothesis results ... WISE Applets This applet converts probability values to z values and vice versa. The simple version converts only right-tail p and z values. The graphic version allows the user to input left-tail p, raw scores, and the mean and standard deviation of the group of interest. Hypothesis Testing Applet Hypothesis tests for a mean Hypothesis tests for a mean. The applet below allows one to visually investigate hypothesis tests for a mean. Specify the sample size, n, the shape of the distribution (Normal or Right skewed), the true population mean (Mean), the true population standard deviation (Std. Dev.), the null value for the mean (Null mean) and the alternative for the test (Alternative). Power of a Hypothesis Test Applet This applet illustrates the fundamental principles of statistical hypothesis testing through the simplest example: the test for the mean of a single normal population, variance known (the Z test).. The basic set-up of the test is this: using only n independent observations X 1, X 2,..., X n from a normal distribution with unknown mean (but known variance), the task is to decide whether or not ... Full article: Two Applets for Teaching Hypothesis Testing Nevertheless, students have good intuition about what makes a thing "too unlikely to be true". This applet guides students to make a decision based on a given probability without introducing formal concepts of hypothesis testing. The applet consists of two "views", called "test view" (. Figure 1. ) and "investigate view" (. Hypothesis Testing The Four Steps in Hypothesis Testing. STEP 1: State the appropriate null and alternative hypotheses, Ho and Ha. STEP 2: Obtain a random sample, collect relevant data, and check whether the data meet the conditions under which the test can be used. If the conditions are met, summarize the data using a test statistic. Hypothesis Testing Applet Open in new window Open in current window Open in current window Confidence intervals, hypothesis testing and p-values tutorial Purpose of the applet To make explicit the correspondence between inference based on confidence intervals (CIs) and formal hypothesis testing using Confidence intervals, hypothesis testing and p-values tutorial - an amiable correspondence Power of a hypothesis test This applet gives a visualisation of the concept of statistical power, and helps illustrate the relationship between power, sample size, standard deviation and ... it has no effect on the hypothesis test.) Other resources: Online tutorial using this applet. Alternate version of the applet with large sample sizes. Geogebratube page for this ... Confidence intervals, hypothesis testing and p-values This applet illustrates the connection between a confidence interval, a formal hypothesis test, and the p-value of a hypothesis test. Conceptual Learning with Interactive Applets. Menu. Confidence intervals, hypothesis testing and p-values Hypothesis Testing Calculator with Steps Hypothesis Testing Calculator. The first step in hypothesis testing is to calculate the test statistic. The formula for the test statistic depends on whether the population standard deviation (σ) is known or unknown. If σ is known, our hypothesis test is known as a z test and we use the z distribution. If σ is unknown, our hypothesis test is ... WISE » Instructor's Guide: Hypothesis Testing Tutorial The Hypothesis Testing (HT) Tutorial assumes that students have some familiarity with basic statistics, such as means, standard deviation, and variance, and are able to calculate standard errors of the mean and z -scores. Students should also have an understanding of the normal distribution, sampling distributions, and the Central Limit Theorem. 10 2A Hypothesis Test for a Proportion Using Coin Flipping Applet Introduces hypothesis test for a population proportion using simulation with a coin-flipping applet. Utilizes the P-value approach. Based on Section 10.2A ... Theory-Based Inference Applet Theory-based inference Applet. Scenario. One proportion One mean Two proportions Two means. Enter data. Paste data. Stacked (Value Group) Includes header. Paste data below: Use Data. 5 Free Resources for Understanding Hypothesis Testing Hypothesis testing is a fundamental concept in statistics and involves making inferences about populations based on sample data. There are a number of free online resources that can help demystify the hypothesis testing process. These range from courses and textbooks to video tutorials, catering to different learning styles and levels of ... Power of a hypothesis test (large sample version) This applet gives a visualisation of the concept of statistical power, and helps illustrate the relationship between power, sample size, standard dev… WISE » Tutorial: Hypothesis Testing Sadly, browsers no longer support the interactive Java applet that is featured in this tutorial. Introduction to Hypothesis Testing. Overview: Statistical hypothesis testing is a method of making decisions about a population based on sample data.We can compute how likely it is to find specific sample data if the sample was drawn randomly from the hypothesized population. Conceptual Learning with Interactive Applets Confidence intervals, hypothesis testing and p-values. This applet illustrates the connection between a confidence interval, a formal hypothesis test, and the p-value of a hypothesis test. 12 Jul 2021 Applets. Power of a hypothesis test. Hypothesis Testing Applet Open in new window Open in current window ... Problem 31 Load the hypothesis tests for a ... [FREE SOLUTION] Load the hypothesis tests for a mean applet. (a) Set the shape to right skewed, the mean to \(50,\) and the standard deviation to \(10 .\) Obtain 1000 simple random samples of size \(n=8\) from this population, and test whether the mean is different from \(50 .\) How many of the samples led to a rejection of the null hypothesis if \(\alpha=0.05 ?\) Rossman/Chance Applet Collection One proportion inference. Goodness of Fit. Analyzing Two-way Tables. Matched Pairs. Randomization test for quantitative response (multiple groups) two means. Randomization test for categorical response (multiple groups) Dolphin Study applet. Power of a hypothesis test This applet gives a visualisation of the concept of statistical power, and helps illustrate the relationship between power, sample size, standard dev… Chi-Square Distribution Applet/Calculator This applet computes probabilities and percentiles for the chi-square distribution: (left) box and press "Tab" or "Enter" on your keyboard. The probability from the drop-down box for a right-tail probability. To determine a percentile, enter the percentile (e.g. use 0.8 for the 80th percentile) in the from the drop-down box, and press "Tab" or ... essay homework paper phd project resume review speech thesis