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Boundless Lecture Slides

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  1. Boundless Lecture Slides Available on the Boundless Teaching Platform Free to share, print, make copies and changes. Get yours at www.boundless.com

  2. Using Boundless Presentations Boundless Teaching Platform Boundless empowers educators to engage their students with affordable, customizable textbooks and intuitive teaching tools. The free Boundless Teaching Platform gives educators the ability to customize textbooks in more than 20 subjects that align to hundreds of popular titles. Get started by using high quality Boundless books, or make switching to our platform easier by building from Boundless content pre-organized to match the assigned textbook. This platform gives educators the tools they need to assign readings and assessments, monitor student activity, and lead their classes with pre-made teaching resources. Get started now at: • The Appendix The appendix is for you to use to add depth and breadth to your lectures. You can simply drag and drop slides from the appendix into the main presentation to make for a richer lecture experience. http://boundless.com/teaching-platform • Free to edit, share, and copy Feel free to edit, share, and make as many copies of the Boundless presentations as you like. We encourage you to take these presentations and make them your own. If you have any questions or problems please email: educators@boundless.com Free to share, print, make copies and changes. Get yours at www.boundless.com

  3. About Boundless • Boundless is an innovative technology company making education more affordable and accessible for students everywhere. The company creates the world’s best open educational content in 20+ subjects that align to more than 1,000 popular college textbooks. Boundless integrates learning technology into all its premium books to help students study more efficiently at a fraction of the cost of traditional textbooks. The company also empowers educators to engage their students more effectively through customizable books and intuitive teaching tools as part of the Boundless Teaching Platform. More than 2 million learners access Boundless free and premium content each month across the company’s wide distribution platforms, including its website, iOS apps, Kindle books, and iBooks. To get started learning or teaching with Boundless, visit boundless.com. Free to share, print, make copies and changes. Get yours at www.boundless.com

  4. Estimation Estimation and Hypothesis Testing Statistical Power Comparing More than Two Means Confidence Intervals ] Hypothesis Testing: One Sample Estimation and Hypothesis Testing Free to share, print, make copies and changes. Get yours at www.boundless.com

  5. Hypothesis Testing: Two Samples Estimation and Hypothesis Testing(continued) Hypothesis Testing: Correlations One-Way ANOVA Two-Way ANOVA ] Repeated-Measures ANOVA Estimation and Hypothesis Testing Free to share, print, make copies and changes. Get yours at www.boundless.com

  6. Estimation and Hypothesis Testing > Estimation Estimation • Estimation • Estimates and Sample Size • Estimating the Target Parameter: Point Estimation • Estimating the Target Parameter: Interval Estimation • Estimating a Population Proportion Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/statistics/textbooks/boundless-statistics-textbook/estimation-and-hypothesis-testing-12/estimation-50/

  7. Estimation and Hypothesis Testing > Statistical Power Statistical Power • Statistical Power Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/statistics/textbooks/boundless-statistics-textbook/estimation-and-hypothesis-testing-12/statistical-power-51/

  8. Estimation and Hypothesis Testing > Comparing More than Two Means Comparing More than Two Means • Elements of a Designed Study • Randomized Design: Single-Factor • Multiple Comparisons of Means • Randomized Block Design • Factorial Experiments: Two Factors Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/statistics/textbooks/boundless-statistics-textbook/estimation-and-hypothesis-testing-12/comparing-more-than-two-means-52/

  9. Estimation and Hypothesis Testing > Confidence Intervals Confidence Intervals • What Is a Confidence Interval? • Interpreting a Confidence Interval • Caveat Emptor and the Gallup Poll • Level of Confidence • Determining Sample Size • Confidence Interval for a Population Proportion • Confidence Interval for a Population Mean, Standard Deviation Known • Confidence Interval for a Population Mean, Standard Deviation Not Known • Estimating a Population Variance Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/statistics/textbooks/boundless-statistics-textbook/estimation-and-hypothesis-testing-12/confidence-intervals-53/

  10. Estimation and Hypothesis Testing > Hypothesis Testing: One Sample Hypothesis Testing: One Sample • Tests of Significance • Elements of a Hypothesis Test • The Null and the Alternative • Type I and Type II Errors • Significance Levels • Directional Hypotheses and One-Tailed Tests • Creating a Hypothesis Test • Testing a Single Proportion • Testing a Single Mean • Testing a Single Variance Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/statistics/textbooks/boundless-statistics-textbook/estimation-and-hypothesis-testing-12/hypothesis-testing-one-sample-54/

  11. Estimation and Hypothesis Testing > Hypothesis Testing: Two Samples Hypothesis Testing: Two Samples • Using Two Samples • Comparing Two Independent Population Means • Comparing Two Independent Population Proportions • Comparing Matched or Paired Samples • Comparing Two Population Variances • Determining Sample Size Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/statistics/textbooks/boundless-statistics-textbook/estimation-and-hypothesis-testing-12/hypothesis-testing-two-samples-55/

  12. Estimation and Hypothesis Testing > Hypothesis Testing: Correlations Hypothesis Testing: Correlations • Hypothesis Tests with the Pearson Correlation Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/statistics/textbooks/boundless-statistics-textbook/estimation-and-hypothesis-testing-12/hypothesis-testing-correlations-56/

  13. Estimation and Hypothesis Testing > One-Way ANOVA One-Way ANOVA • The F-Test • The One-Way F-Test • Variance Estimates • Mean Squares and the F-Ratio • ANOVA • ANOVA Design • ANOVA Assumptions Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/statistics/textbooks/boundless-statistics-textbook/estimation-and-hypothesis-testing-12/one-way-anova-57/

  14. Estimation and Hypothesis Testing > Two-Way ANOVA Two-Way ANOVA • Two-Way ANOVA Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/statistics/textbooks/boundless-statistics-textbook/estimation-and-hypothesis-testing-12/two-way-anova-58/

  15. Estimation and Hypothesis Testing > Repeated-Measures ANOVA Repeated-Measures ANOVA • Repeated Measures Design • Further Discussion of ANOVA Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/statistics/textbooks/boundless-statistics-textbook/estimation-and-hypothesis-testing-12/repeated-measures-anova-59/

  16. Appendix Free to share, print, make copies and changes. Get yours at www.boundless.com

  17. Estimation and Hypothesis Testing Key terms • alternative hypothesisa rival hypothesis to the null hypothesis, whose likelihoods are compared by a statistical hypothesis test • ANOVAAnalysis of variance—a collection of statistical models used to analyze the differences between group means and their associated procedures (such as "variation" among and between groups). • ANOVAAnalysis of variance—a collection of statistical models used to analyze the differences between group means and their associated procedures (such as "variation" among and between groups). • ANOVAAnalysis of variance—a collection of statistical models used to analyze the differences between group means and their associated procedures (such as "variation" among and between groups). • ANOVAAnalysis of variance—a collection of statistical models used to analyze the differences between group means and their associated procedures (such as "variation" among and between groups). • ANOVAAnalysis of variance—a collection of statistical models used to analyze the differences between group means and their associated procedures (such as "variation" among and between groups). • ANOVAAnalysis of variance—a collection of statistical models used to analyze the differences between group means and their associated procedures (such as "variation" among and between groups). • ANOVAAnalysis of variance—a collection of statistical models used to analyze the differences between group means and their associated procedures (such as "variation" among and between groups). • blockingA schedule for conducting treatment combinations in an experimental study such that any effects on the experimental results due to a known change in raw materials, operators, machines, etc., become concentrated in the levels of the blocking variable. • blockingA schedule for conducting treatment combinations in an experimental study such that any effects on the experimental results due to a known change in raw materials, operators, machines, etc., become concentrated in the levels of the blocking variable. • Bonferroni correctiona method used to counteract the problem of multiple comparisons; considered the simplest and most conservative method to control the familywise error rate • Boole's inequalitya probability theory stating that for any finite or countable set of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the individual events Free to share, print, make copies and changes. Get yours at www.boundless.com

  18. Estimation and Hypothesis Testing • caveat emptorLatin for "let the buyer beware"—the property law principle that controls the sale of real property after the date of closing, but may also apply to sales of other goods. • central limit theoremThe theorem that states: If the sum of independent identically distributed random variables has a finite variance, then it will be (approximately) normally distributed. • chi-square distributionWith degrees of freedom, the distribution of a sum of the squares of independent standard normal random variables. • Cohen's DA measure of effect size indicating the amount of different between two groups on a construct of interest in standard deviation units. • confidence intervalA type of interval estimate of a population parameter used to indicate the reliability of an estimate. • confidence intervalA type of interval estimate of a population parameter used to indicate the reliability of an estimate. • confidence intervalA type of interval estimate of a population parameter used to indicate the reliability of an estimate. • confidence intervalA type of interval estimate of a population parameter used to indicate the reliability of an estimate. • confidence intervalA type of interval estimate of a population parameter used to indicate the reliability of an estimate. • confidence levelThe probability that a measured quantity will fall within a given confidence interval. • critical valuethe value corresponding to a given significance level • degree of freedomAny unrestricted variable in a frequency distribution. Free to share, print, make copies and changes. Get yours at www.boundless.com

  19. Estimation and Hypothesis Testing • degrees of freedom (df)The number of objects in a sample that are free to vary. • dfNotation for degrees of freedom. • errorThe difference between the population parameter and the calculated sample statistics. • error boundThe margin or error that depends on the confidence level, sample size, and the estimated (from the sample) proportion of successes. • F distributionA probability distribution of the ratio of two variables, each with a chi-square distribution; used in analysis of variance, especially in the significance testing of a correlation coefficient ( squared). • F-TestA statistical test using the distribution, most often used when comparing statistical models that have been fitted to a data set, in order to identify the model that best fits the population from which the data were sampled. • F-Testa statistical test using the distribution, most often used when comparing statistical models that have been fitted to a data set, in order to identify the model that best fits the population from which the data were sampled • F-TestA statistical test using the F-distribution, most often used when comparing statistical models that have been fitted to a data set, in order to identify the model that best fits the population from which the data were sampled. • factorThe explanatory, or independent, variable in an experiment. • factorThe explanatory, or independent, variable in an experiment. • frequentistAn advocate of frequency probability. • homoscedasticif all random variables in a sequence or vector have the same finite variance Free to share, print, make copies and changes. Get yours at www.boundless.com

  20. Estimation and Hypothesis Testing • homoscedasticityA property of a set of random variables where each variable has the same finite variance. • independent groupA statistical group of random variables that has the same probability distribution as the others, and that are all mutually independent. • independent sampleTwo samples are independent as they are drawn from two different populations, and the samples have no effect on each other. • interval estimateA range of values used to estimate a population parameter. • iterativeOf a procedure that involves repetition of steps (iteration) to achieve the desired outcome. • law of large numbersThe statistical tendency toward a fixed ratio in the results when an experiment is repeated a large number of times. • levelThe specific value of a factor in an experiment. • levelThe specific value of a factor in an experiment. • longitudinal studyA correlational research study that involves repeated observations of the same variables over long periods of time. • margin of errorAn expression of the lack of precision in the results obtained from a sample. • margin of errorAn expression of the lack of precision in the results obtained from a sample. • margin of errorAn expression of the lack of precision in the results obtained from a sample. Free to share, print, make copies and changes. Get yours at www.boundless.com

  21. Estimation and Hypothesis Testing • margin of errorAn expression of the lack of precision in the results obtained from a sample. • matched pairA data set of two groups consisting of two samples that are dependent. • Mead's resource equation: an equation that gives a hint of what the appropriate sample size is, where parameters such as expected standard deviations or expected differences in values between groups are unknown or very hard to estimate. • nuisance factorsVariables that may affect the measured results, but are not of primary interest. • null hypothesisA hypothesis set up to be refuted in order to support an alternative hypothesis; presumed true until statistical evidence in the form of a hypothesis test indicates otherwise. • null hypothesisA hypothesis set up to be refuted in order to support an alternative hypothesis; presumed true until statistical evidence in the form of a hypothesis test indicates otherwise. • null hypothesisA hypothesis set up to be refuted in order to support an alternative hypothesis; presumed true until statistical evidence in the form of a hypothesis test indicates otherwise. • null hypothesisA hypothesis set up to be refuted in order to support an alternative hypothesis; presumed true until statistical evidence in the form of a hypothesis test indicates otherwise. • null hypothesisA hypothesis set up to be refuted in order to support an alternative hypothesis; presumed true until statistical evidence in the form of a hypothesis test indicates otherwise. • null hypothesisA hypothesis set up to be refuted in order to support an alternative hypothesis; presumed true until statistical evidence in the form of a hypothesis test indicates otherwise. • null hypothesisA hypothesis set up to be refuted in order to support an alternative hypothesis; presumed true until statistical evidence in the form of a hypothesis test indicates otherwise. • null hypothesisA hypothesis set up to be refuted in order to support an alternative hypothesis; presumed true until statistical evidence in the form of a hypothesis test indicates otherwise. Free to share, print, make copies and changes. Get yours at www.boundless.com

  22. Estimation and Hypothesis Testing • null hypothesisA hypothesis set up to be refuted in order to support an alternative hypothesis; presumed true until statistical evidence in the form of a hypothesis test indicates otherwise. • null hypothesisA hypothesis set up to be refuted in order to support an alternative hypothesis; presumed true until statistical evidence in the form of a hypothesis test indicates otherwise. • null hypothesisA hypothesis set up to be refuted in order to support an alternative hypothesis; presumed true until statistical evidence in the form of a hypothesis test indicates otherwise. • null hypothesisA hypothesis set up to be refuted in order to support an alternative hypothesis; presumed true until statistical evidence in the form of a hypothesis test indicates otherwise. • null hypothesisA hypothesis set up to be refuted in order to support an alternative hypothesis; presumed true until statistical evidence in the form of a hypothesis test indicates otherwise. • omnibuscontaining multiple items • one-tailed hypothesisa hypothesis in which the value of a parameter is specified as being either above or equal to a certain value or below or equal to a certain value • order effectAn effect that occurs when a participant in an experiment is able to perform a task and then perform it again at some later time. • orthogonalstatistically independent, with reference to variates • p-valueThe probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true. • Pearson's correlation coefficienta measure of the linear correlation (dependence) between two variables and , giving a value between and inclusive, where 1 is total positive correlation, 0 is no correlation, and is negative correlation • point estimatea single value estimate for a population parameter Free to share, print, make copies and changes. Get yours at www.boundless.com

  23. Estimation and Hypothesis Testing • point estimatea single value estimate for a population parameter • pooled varianceA method for estimating variance given several different samples taken in different circumstances where the mean may vary between samples but the true variance is assumed to remain the same. • populationa group of units (persons, objects, or other items) enumerated in a census or from which a sample is drawn • random samplea sample randomly taken from an investigated population • samplea subset of a population selected for measurement, observation, or questioning to provide statistical information about the population • significance criteriona statement of how unlikely a positive result must be, if the null hypothesis of no effect is true, for the null hypothesis to be rejected • significance levelA measure of how likely it is to draw a false conclusion in a statistical test, when the results are really just random variations. • simple random sampleA sample in which each individual is chosen randomly and entirely by chance, such that each individual has the same probability of being chosen at any stage during the sampling process, and each subset of individuals has the same probability of being chosen for the sample as any other subset of individuals. • sphericityA statistical assumption requiring that the variances for each set of difference scores are equal. • standard errorA measure of how spread out data values are around the mean, defined as the square root of the variance. • statistical significanceA measure of how unlikely it is that a result has occurred by chance. • Stratified SamplingA method of sampling that involves dividing members of the population into homogeneous subgroups before sampling. Free to share, print, make copies and changes. Get yours at www.boundless.com

  24. Estimation and Hypothesis Testing • Student's t-testAny statistical hypothesis test in which the test statistic follows a Student's distribution if the null hypothesis is supported. • t-distributiona family of continuous probability disrtibutions that arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard devition is unknown • t-scoreA score utilized in setting up norms for standardized tests; obtained by linearly transforming normalized standard scores. • two-way ANOVAan extension of the one-way ANOVA test that examines the influence of different categorical independent variables on one dependent variable • Type I errorAn error occurring when the null hypothesis (H0) is true, but is rejected. • Type I errorAn error occurring when the null hypothesis (H0) is true, but is rejected. • Type I errorRejecting the null hypothesis when the null hypothesis is true. • Type I errorRejecting the null hypothesis when the null hypothesis is true. • type II errorAccepting the null hypothesis when the null hypothesis is false. • unit-treatment additivityAn assumption that states that the observed response from the experimental unit when receiving treatment can be written as the sum of the unit's response and the treatment-effect . • variancea measure of how far a set of numbers is spread out • variancea measure of how far a set of numbers is spread out Free to share, print, make copies and changes. Get yours at www.boundless.com

  25. Estimation and Hypothesis Testing Sample Size This image shows the formula used to calculate an appropriate sample size. Free to share, print, make copies and changes. Get yours at www.boundless.com OpenStax CNX."Susan Dean and Barbara Illowsky, Confidence Intervals: Confidence Interval for a Population Proportion. June 6, 2013."CC BY 3.0http://cnx.org/content/m16963/latest/View on Boundless.com

  26. Estimation and Hypothesis Testing Sir Ronald Fisher Sir Ronald Fisher was an English statistician, evolutionary biologist, geneticist, and eugenicist who standardized the interpretation of statistical significance (starting around 1925), and was the main driving force behind the popularity of tests of significance in empirical research, especially in the social and behavioral sciences. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikimedia."R.A. Fischer."CC BY-SAhttp://commons.wikimedia.org/wiki/File:R._A._Fischer.jpgView on Boundless.com

  27. Estimation and Hypothesis Testing Two-Tailed Statistical Test This image shows a graph representation of a two-tailed hypothesis test. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikispaces."Econ-Stat-Media - Hypothesis Testing- Chap 13-17 in p-value."CC BY-SAhttp://econ-stat-media.wikispaces.com/Hypothesis+Testing-++Chap+13-17+in+p-valueView on Boundless.com

  28. Estimation and Hypothesis Testing Critical Region This image shows a graph of the critical region for the test statistic in our example. Free to share, print, make copies and changes. Get yours at www.boundless.com OpenStax CNX."Irene Mary Duranczyk, Suzanne Loch, and Janet Stottlemyer, Hypotheses Testing: Two Column Model Step by Step Example of a Hypothesis Test for a Single Proportion. June 11, 2013."CC BY 3.0http://cnx.org/content/m46731/latest/View on Boundless.com

  29. Estimation and Hypothesis Testing The Population Mean This image shows a series of histograms for a large number of sample means taken from a population. Recall that as more sample means are taken, the closer the mean of these means will be to the population mean. In this section, we explore hypothesis testing of two independent population means (and proportions) and also tests for paired samples of population means. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikimedia."Empirical CLT - Figure - 040711."CC BY-SAhttp://commons.wikimedia.org/wiki/File:Empirical_CLT_-_Figure_-_040711.jpgView on Boundless.com

  30. Estimation and Hypothesis Testing Independent Sample Table 1 This table lays out the parameters for our example. Free to share, print, make copies and changes. Get yours at www.boundless.com OpenStax CNX."Susan Dean and Barbara Illowsky, Hypothesis Testing: Two Population Means and Two Population Proportions: Comparing Two Independent Population Means with Unknown Population Standard Deviations. June 11, 2013."CC BY 3.0http://cnx.org/content/m17025/latest/View on Boundless.com

  31. Estimation and Hypothesis Testing Observed Response, Unit-Treatment Additivity This equation is the sum of an observed unit's response and the treatment effect. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Analysis of variance."CC BY-SAhttps://en.wikipedia.org/wiki/Analysis_of_varianceView on Boundless.com

  32. Estimation and Hypothesis Testing Eta-Squared Eta-squared is equal to the treated sample size divided by the total sample size. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Analysis of variance."CC BY-SAhttps://en.wikipedia.org/wiki/Analysis_of_varianceView on Boundless.com

  33. Estimation and Hypothesis Testing ANOVA Calculation Table This table summarizes the calculations necessary in an ANOVA for comparing multiple means. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikidot."Chapter 10 Hypothesis Tests - Statistics."CC BY-SAhttp://statistics.wikidot.com/ch10#toc4View on Boundless.com

  34. Estimation and Hypothesis Testing Factorial Notation This table shows the notation used for a 2x2 factorial experiment. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Factorial experiment."GNU FDLhttp://en.wikipedia.org/wiki/Factorial_experimentView on Boundless.com

  35. Estimation and Hypothesis Testing Power Curve 1 This graph shows the true probability of heads when flipping a coin 10 times. Free to share, print, make copies and changes. Get yours at www.boundless.com Alex Reinhart."Statistical power and underpowered statistics — Statistics Done Wrong."CC BYhttp://www.refsmmat.com/statistics/power.htmlView on Boundless.com

  36. Estimation and Hypothesis Testing Power Curve 2 This graph shows the true probability of heads when flipping a coin 100 times. Free to share, print, make copies and changes. Get yours at www.boundless.com Alex Reinhart."Statistical power and underpowered statistics — Statistics Done Wrong."CC BYhttp://www.refsmmat.com/statistics/power.htmlView on Boundless.com

  37. Estimation and Hypothesis Testing Power Curve 3 This graph shows the true probability of heads when flipping a coin 1,000 times. Free to share, print, make copies and changes. Get yours at www.boundless.com Alex Reinhart."Statistical power and underpowered statistics — Statistics Done Wrong."CC BYhttp://www.refsmmat.com/statistics/power.htmlView on Boundless.com

  38. Estimation and Hypothesis Testing ANOVA With Very Good Fit This graph is a representation of a situation with a very good fit in terms of ANOVA statistics Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."ANOVA very good fit."CC BY-SAhttps://en.wikipedia.org/wiki/File:ANOVA_very_good_fit.jpgView on Boundless.com

  39. Estimation and Hypothesis Testing Excel Solution This image shows the solution to our ANOVA example performed in Excel. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikidot."Chapter 10 Hypothesis Tests - Statistics."CC BY-SAhttp://statistics.wikidot.com/ch10#toc4View on Boundless.com

  40. Estimation and Hypothesis Testing Sample Size Determination This table can be used in a two-sample -test to estimate the sample sizes of an experimental group and a control group that are of equal size. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Sample size determination."GNU FDLhttp://en.wikipedia.org/wiki/Sample_size_determinationView on Boundless.com

  41. Estimation and Hypothesis Testing Graphical Representation This figure is a graphical representation of the confidence interval we calculated in this example. Free to share, print, make copies and changes. Get yours at www.boundless.com OpenStax CNX."Irene Mary Duranczyk, Suzanne Loch, and Janet Stottlemyer, Confidence Interval: Two Column Model Step by Step Example of a Confidence Interval for a Mean, Sigma Unknown June 6, 2013."CC BY 3.0http://cnx.org/content/m46277/latest/View on Boundless.com

  42. Estimation and Hypothesis Testing Confidence Interval In this bar chart, the top ends of the bars indicate observation means and the red line segments represent the confidence intervals surrounding them. Although the bars are shown as symmetric in this chart, they do not have to be symmetric. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Confidenceinterval."CC BY-SAhttp://en.wikipedia.org/wiki/File:Confidenceinterval.pngView on Boundless.com

  43. Estimation and Hypothesis Testing Error Bound Population This image shows the formula used to calculate the error bound population. Free to share, print, make copies and changes. Get yours at www.boundless.com OpenStax CNX."Susan Dean and Barbara Illowsky, Confidence Intervals: Confidence Interval for a Population Proportion. June 6, 2013."CC BY 3.0http://cnx.org/content/m16963/latest/View on Boundless.com

  44. Estimation and Hypothesis Testing Confidence Level This image shows values used in our example. Free to share, print, make copies and changes. Get yours at www.boundless.com OpenStax CNX."Irene Mary Duranczyk, Suzanne Loch, and Janet Stottlemyer, Confidence Interval: Two Column Model Step by Step Example of a Confidence Interval for a Mean, Sigma Known. June 6, 2013."CC BY 3.0http://cnx.org/content/m46276/latest/View on Boundless.com

  45. Estimation and Hypothesis Testing Left Endpoint This figure shows the calculation for the left endpoint for the confidence interval in our example. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikispaces."coachwill - 9.5 Confidence Interval for Variance WS.docx - Links."CC BY-SAhttp://coachwill.wikispaces.com/file/links/9.5+Confidence+Interval+for+Variance+WS.docxView on Boundless.com

  46. Estimation and Hypothesis Testing Block Design An example of a blocked design, where the blocking factor is gender. Free to share, print, make copies and changes. Get yours at www.boundless.com Education.com."Experiments and Observational Studies for AP Statistics | Education.com."CC BYhttp://www.education.com/study-help/article/experiments-observational-studies/View on Boundless.com

  47. Estimation and Hypothesis Testing ANOVA With No Fit This graph shows a representation of a situation with no fit at all in terms of ANOVA statistics. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."ANOVA no fit."CC BY-SAhttps://en.wikipedia.org/wiki/File:ANOVA_no_fit.jpgView on Boundless.com

  48. Estimation and Hypothesis Testing Two-Tailed Test A two-tailed test corresponds to both extreme negative and extreme positive directions of the test statistic, here the normal distribution. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikimedia."DisNormal06."Public domainhttp://commons.wikimedia.org/wiki/File:DisNormal06.svgView on Boundless.com

  49. Estimation and Hypothesis Testing Confidence Level In this bar chart, the top ends of the bars indicate observation means and the red line segments represent the confidence intervals surrounding them. Although the bars are shown as symmetric in this chart, they do not have to be symmetric. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Confidence interval."GNU FDLhttp://en.wikipedia.org/wiki/Confidence_intervalView on Boundless.com

  50. Estimation and Hypothesis Testing -Distribution The ratio follows the -distribution, which is right skewed. Free to share, print, make copies and changes. Get yours at www.boundless.com OpenStax CNX."Barbara Illowsky and Susan Dean, Collaborative Statistics. June 14, 2013."CC BY 3.0http://cnx.org/content/m17062/latest/View on Boundless.com

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