Lecture_7

# Lecture_7 - Statistical Inference: Significance Tests About...

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1 Statistical Inference: Significance Tests About Hypotheses What Are the Steps for Performing a Significance Test?

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2 Learning Objectives 1. 5 Steps of a Significance Test 2. Assumptions 3. Hypotheses 4. Calculate the test statistic 5. P-Value 6. Conclusion and Statistic Significance
The Process of Hypothesis Testing Assume the population mean age is 50. ( ) REJECT Identify the Population Take a Sample Null Hypothesis No, not likely! X 20 likely if Is ? μ = = 50 0 : 50 H μ= ( 29 20 X =

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4 Learning Objective 1 : Significance Test A significance test is a method of using data to summarize the evidence about a hypothesis A significance test about a hypothesis has five steps 1. Assumptions 2. Hypotheses 3. Test Statistic 4. P-value 5. Conclusion
5 Learning Objective 2 : Step 1: Assumptions A (significance) test assumes that the data production used randomization Other assumptions may include: Assumptions about the sample size Assumptions about the shape of the population distribution

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6 Learning Objective 3 : Step 2: Hypothesis A hypothesis is a statement about a population, usually of the form that a certain parameter takes a particular numerical value or falls in a certain range of values The main goal in many research studies is to check whether the data support certain hypotheses
7 Learning Objective 3: Step 2: Hypotheses Each significance test has two hypotheses: H 0 : The null hypothesis is a statement that the parameter takes a particular value. It has a single parameter value. H a : The alternative hypothesis states that the parameter falls in some alternative range of values. (researcher wants to prove)

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8 Learning Objective 3: Null and Alternative Hypotheses The value in the null hypothesis usually represents no effect The symbol H o denotes null hypothesis The value in the alternative hypothesis usually represents an effect of some type The symbol H a denotes alternative hypothesis The alternative hypothesis should express what the researcher hopes to show. The hypotheses should be formulated before viewing or analyzing the data!
9 Example: You are in charge of quality control in your food company. You sample randomly four packs of cherry tomatoes, each labeled 1/2 lb. (227 g). The average weight from your four boxes is 222 g. Obviously, we cannot expect boxes filled with whole tomatoes to all weigh exactly half a pound. Thus: Is the somewhat smaller weight simply due to chance variation? Is it evidence that the calibrating machine that sorts cherry tomatoes into packs needs revision? Weight of cherry tomato packs: H 0 : µ = 227 g ( µ is the average weight of the population of packs) H a : µ ≠ 227 g ( µ is either larger or smaller) Note: In the alternative, just proving not equal to. However, depending on question, may choose ≤ or ≥ If the question does not specify the usage of ≤ or ≥ then use

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Tests to determine the conclusion  (2 methods) 1. P -value method Comparing to α (alpha) 1.
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## Lecture_7 - Statistical Inference: Significance Tests About...

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