review2500_4slides - Notes Introduction to Probability and...

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Introduction to Probability and Statistics II Instructor: John Snyder Office: Middlebush 35 Office hours: MW 8am - 9:30am Email: [email protected] January 18, 2016 John Snyder (MU) Stat —— 3500 January 18, 2016 1 / 30 Review of STAT 2500 1 Elements of Hypothesis Testing 2 Hypothesis tests for μ 3 Observed Significance Levels: p -Values 4 t -distribution and F -distribution 5 Confidence intervals John Snyder (MU) Stat —— 3500 January 18, 2016 2 / 30 Elements of Hypothesis Testing 1 Elements of Hypothesis Testing 2 Hypothesis tests for μ 3 Observed Significance Levels: p -Values 4 t -distribution and F -distribution 5 Confidence intervals John Snyder (MU) Stat —— 3500 January 18, 2016 3 / 30 Elements of Hypothesis Testing Introduction Data is all around us. We often to use the information in our data to make some statement about the population(s) as a whole. This is known as Hypothesis testing . Does the average consumer spend $100/month on their cell phone bill? Does a certain school program increase standardized test scores? There are many types of hypothesis tests, and new ones are being developed every day for highly specific applications. Here we will be going over some of the tests covered in STAT2500. John Snyder (MU) Stat —— 3500 January 18, 2016 3 / 30 Notes Notes Notes Notes
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Elements of Hypothesis Testing The Hypothesis Hypothesis testing involves making a decision about the true nature of some characteristic of the population using the data as evidence for or against our research question. There are two pieces in the statement of a hypothesis test. 1 The null hypothesis( H 0 ), which is what we go into the study believing, and the belief we will fall back on should our results be ”null.” 2 The alternative hypothesis( H a ), which is what we desire to show to be true. John Snyder (MU) Stat —— 3500 January 18, 2016 4 / 30 Elements of Hypothesis Testing The Procedure The typical steps in performing a hypothesis test are the following. 1 Specify the hypothesis. 2 Collect evidence in the form of data. Sample mean, standard deviation, etc 3 Apply some mathematical function to this data that ends up giving you a number that comes from a distribution, this is called a test statistic Obviously the formulas have already been developed by statisticians, but this is where we get the ”z-value”, ”t-value”, ”F-statistic”, etc. 4 Use this number to get a ”p-value” for the test or find a rejection region(from a table) to determine if this number is unrealistic given the null hypothesis is true. 5 Make a conclusion by Rejecting or Accepting H 0 . John Snyder (MU) Stat —— 3500 January 18, 2016 5 / 30 Elements of Hypothesis Testing Rejection Region Rejection Region The set of numerical values for the test statistic that will lead us to reject the null hypothesis in favor of the alternative hypothesis .
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