Lecture22_HypothesisTest2

# Lecture22_HypothesisTest2 - ECE 340 Probabilistic Methods...

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ECE 340 Probabilistic Methods in Engineering M/W 3-4:15 Prof. Vince Calhoun Prof. Vince Calhoun Lecture 22: Hypothesis Testing II Lecture 22: Hypothesis Testing II

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Hypothesis Tests • If the population variance is unknown, use s of the sample to approximate population variance, since under central limit theorem, s = σ when n > 30. Thus solve the problem as before, using s • With smaller sample sizes, we have a different problem. But it is solved in the same manner. Instead of using the z distribution, we use the t distribution
Hypothesis Tests • Using t distribution when: • Sample is small (<30) • Parent population is essentially normal • Population variance ( σ ) is unknown • As n decreases, variation within the sample increases, so distribution becomes flatter.

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Methods to Test a Statistical Hypothesis 1) Calculate Test Statistics, check if it falls in expected value range, make conclusion based upon the result (hypothesis test). 2) Calculate confidence interval. If H 0 : μ = μ 0 falls in interval, fail to reject the null hypothesis H 0 3) P-value for an event Reject H 0 if p-value α = significant level. If p-value < α , reject H 0 If p-value α , fail to reject
Methods to Test a Statistical Hypothesis Calculate Test Statistics, Test if it falls in Critical Region (CR), make conclusion (hypothesis test). If Test Statistic > CR, reject H 0 Calculate confidence interval. If μ 0 falls in interval, fail to reject the null hypothesis H 0 Calculate Test Statistic, Calculate p-value. If p-value < α , reject H 0

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Relationship Between Hypothesis Tests and Confidence Intervals For a two-sided hypothesis test: H 0 : μ = μ 0 H a : μ μ 0 Equivalent confidence interval is: (lower-limit, upper-limit) If μ 0 is contained within the two-sided interval you will fail to reject H 0 If μ 0 is not contained within the two-sided interval you will reject H 0
Relationship Between Hypothesis Tests and Confidence Intervals i. For an upper-tail test: H 0 : μ = μ 0 H a : μ > μ 0 Equivalent confidence interval is: (lower-limit,

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## This note was uploaded on 02/10/2010 for the course TBE 2300 taught by Professor Cudeback during the Spring '10 term at Webber.

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Lecture22_HypothesisTest2 - ECE 340 Probabilistic Methods...

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