Lecture17_ch8

# Lecture17_ch8 - STAT 350 Lecture 17 8.2 Tests Concerning...

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STAT 350 Lecture 17 8.2 Tests Concerning Hypotheses About Means

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Hypotheses Testing Confidence Intervals estimate an unknown population parameter. give a range of values where we think the true parameter lies. Hypothesis Tests assess the evidence provided by the data in favor of or against some claim (called a hypothesis) about the population
8.1 Hypotheses and Test Procedures A statistical hypothesis is a claim or assertion about a population parameter(s) Example Parameter: π =proportion of e-mails from a certain system that are undeliverable Hypothesis: π <0.01 (or 1%)

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Example of Statistical Hypotheses Parameters: μ 1 = true average lifetime for a particular name-brand tire (miles) μ 2 = true average lifetime for a less expansive store-brand tire (miles) Hypothesis: μ 1- μ 2>10,000 (miles)
Statement of Hypotheses Statistical Hypothesis: On the parameters in a population NOT on the statistics of the sample data Example (ex 1 from 8.1): State whether each of the following assertion is a legitimate statistical hypothesis and why? A) H: σ >100 B) H: C) H: D)H: s 0.50 E) H: σ 1/ σ 2 < 1 45 X 2.0 

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What is a test of hypotheses ? A method for using sample data to decide between the two competing hypotheses under consideration Consider: What does the hypothesis say about the parameter? What does the sample suggest about the parameter? Do they agree or disagree? The results of a test measures how well the data and the hypothesis agree .
Null and Alternative Hypotheses Two hypotheses in a testing of hypotheses: H 0 :the null hypothesis H a : the alternative hypothesis [Definitions] H 0 -- The null hypothesis is the assertion that is initially assumed to be true. H a -- The alternative hypothesis is the claim that contradictory to H 0

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Null Hypothesis The null hypothesis will be rejected in favor of the alternative hypothesis only if sample evidence suggests that H 0 is false. If the sample does not strongly contradict H 0, we will continue to believe in the truth of the null hypothesis. The test of significance is designed to assess the strength of the evidence against the null hypothesis.
Example (ex 3 of 8.1) Many older homes have electrical system that use fuses rather than circuit breakers. A manufacturer of 40-amps fuses wants to make sure that the true average amperage at which its fuses burns out is indeed 40. What null and alternative hypotheses would be of interest to the manufacture?

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Example (ex 3 from ch8.1) Many older homes have electrical system that use fuses rather than circuit breakers. A manufacturer of 40-amps fuses wants to make sure that the true average amperage at which its fuses burns out is indeed 40.
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## This note was uploaded on 04/23/2011 for the course STAT 350 taught by Professor Staff during the Spring '08 term at Purdue.

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Lecture17_ch8 - STAT 350 Lecture 17 8.2 Tests Concerning...

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