Scenarios for the Null Hypothesis and Alternative...

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Instructor: Danny Tran Math 10 Chapter 9 Notes Hypothesis Testing: Single Population Objectives: - Differentiate between Type I & Type II Errors - Describe hypothesis testing in general & in practice - Conduct & interpret hypothesis tests for a single population mean, population SD known. - Conduct & interpret hypothesis tests for a single population mean, population SD unknown. - Conduct & interpret hypothesis tests for a single population proportion. Coin Flipping Activity: Goal: To determine if we can conclude that Danny s special coins are biased. Directions: Flip Danny s coin 10 times, and complete the table: Number of Heads: X = Number of Coin Flips: n = 10 Sample Proportion of Heads: ˆ X p n = = Class Totals: Number of Heads: X = Number of Coin Flips: n = Sample Proportion of Heads: ˆ X p n = = To set up a hypothesis test to determine whether Danny s special coins are biased, we state the null hypothesis and alternative hypothesis. Null Hypothesis 0 H : It is a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt. Alternative Hypothesis A H : It is a claim about the population that is contradictory to 0 H and what we conclude when we reject 0 H .
Scenarios for the Null Hypothesis and Alternative Hypothesis: 0 H A H Equal ( ) = Not Equal ( ) Greater Than Or Equal To ( ) Less Than ( ) Less Than Or Equal To ( ) Greater Than ( ) We will assume that the null hypothesis is true, UNLESS we have enough evidence to prove otherwise. We will use the sample data to calculate the actual probability of getting the test result, called the p-value. Define: The p-value is the probability that, if the null hypothesis is true, the results from another randomly selected sample will be as extreme or more extreme as the results obtained from the given sample.

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