STAT 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 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 output Chapter 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 1 100 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 Type I error o alpha probability of making a Type I error Type II error o 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 o Probability of correctly rejecting a false null hypothesis o Dependence on 1 2 sample size and 3 how different from the null hypothesized value is from the truth Chapter 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 output Chapter 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 output
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