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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