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UT Knoxville STAT 201 - Exam 3 Topics

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Miscellaneous topics from prior chapters:Chapter 19: Confidence Intervals for ProportionsChapter 20: Testing Hypotheses for ProportionsChapter 21: More about TestsChapter 23: Inferences about MeansChapter 24: Comparing Means for Independent SamplesSTAT 201: INTRODUCTION TO STATISTICS FINAL EXAM TOPICS – SPRING 2014 Miscellaneous topics from prior chapters: • Know the difference between a population and a sample • Know what y and µ represent • Have a general understanding of what a sampling distribution is • Given the mean and standard deviation of a population, be able to calculate the mean and standard deviation of the sampling distribution of y (given the sample size n) Chapter 19: Confidence Intervals for Proportions • Standard error for proportions o How it is related to the standard deviation for proportions • Being able to calculate a confidence interval with the aid of the formula sheet • Meaning of confidence • Margin of error • Trade-off between certainty and precision in confidence intervals • Critical values o Being able to read the output of this applet http://davidmlane.com/hyperstat/z_table.html • Assumptions o Independence  Randomization  10% condition o Success/Failure condition • Interpreting JMP outputChapter 20: Testing Hypotheses for Proportions • Hypothesis testing for a single proportion o Null hypothesis o Alternative hypotheses  One sided and two-sided o Ability to set the correct null and alternative hypotheses from a word problem • Assumptions o Independence assumption  Randomization condition  10% condition o Success/Failure condition • Reasoning of hypothesis testing o Interpretation of a P-value in general o Interpretation of large and small P-values o A sufficiently small p-value could mean  (1) that the null hypothesis is true and data was observed that is very improbable under this hypothesis or (2) that the null hypothesis is false  We choose to believe (2) and reject the null hypothesis • Mechanics of calculation using the formula sheet • Sketching a picture of a distribution and the P-value, based on the test statistic and the alternative hypothesis • Interpreting JMP output Chapter 21: More about Tests • Interpretation of p-values in general • Alpha levels • Practical vs. statistical significance • Relationship of hypothesis tests with confidence intervals o A (1-α)100% confidence interval can be interpreted as the set of all null hypothesized values that one would not reject in a two-side test with an alpha level of α • Type I error o α = alpha = probability of making a Type I error • Type II error o β = beta = probability of making a Type II error • Trade-offs between alpha and beta o Decreasing the probability of both errors can be done only by increasing the sample size • Power o 1-β o Probability of correctly rejecting a false null hypothesis o Dependence on (1) α, (2) sample size, and (3) how different from the null hypothesized value is from the truthChapter 23: Inferences about Means • Central limit theorem • Standard error of the sample mean o Relationship to standard deviation • Calculation of confidence intervals using the formula sheet • What confidence means • Assumptions o Independence  Random sample  10% condition o Nearly normal condition  How important it is depending on the sample size • Setting up a test of hypothesis from a word problem o One-sided or two-sided alternatives? • P-Value interpretation and calculation o t-Distribution • JMP output Chapter 24: Comparing Means for Independent Samples • Standard error for the difference of sample means o Relationship to standard deviation • Confidence Intervals o Interpretation o Calculations using the formula sheet • Assumptions o Independence  Random sample  10% condition o Nearly normal condition o The groups must have been selected independently of each other • t-test for the difference of two means • Setting up null and alternative hypotheses from a word problem • Interpreting JMP outputChapter 26: Comparing Counts • Chi-Square test of independence • Hypotheses for Chi-square test o Null o Alternative o Why test is always one-sided o Setting them up from a word problem • Assumptions o Categorical data o Random selection of sampling units o Cell expected counts assuming the null hypothesis is true of more than 5 o Being able to determine if they are being met in a word problem • Calculations o Row, column and table totals o Expected counts o Cell Chi^2  What it means when this is large o Chi-square statistic  What it means when this is large o Difference between observed and expectation • Being able to determine why a null hypothesis is rejected o From Mosaic plot (or from cell Chi^2’s) • P-Value calculation set up • Being able to read the output of this applet http://www.stat.tamu.edu/~west/applets/chisqdemo.html • Chi-square and causation • Interpreting JMP


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UT Knoxville STAT 201 - Exam 3 Topics

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