Hypothesis_Testing

# Hypothesis_Testing - Hypothesis Testing Hypothesis testing...

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Hypothesis Testing

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2 Hypothesis testing is used to make decisions concerning the value of a parameter.
3 Null Hypothesis: H 0 a working hypothesis about the population parameter in question

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4 The value specified in the null hypothesis is often: a historical value a claim a production specification
5 Alternate Hypothesis: H 1 any hypothesis that differs from the null hypothesis

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6 An alternate hypothesis is constructed in such a way that it is the one to be accepted when the null hypothesis must be rejected.
7 A manufacturer claims that their light bulbs burn for an average of 1000 hours. We have reason to believe that the bulbs do not last that long. Determine the null and alternate hypotheses .

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8 A manufacturer claims that their light bulbs burn for an average of 1000 hours. . .. The null hypothesis (the claim) is that the true average life is 1000 hours. H 0 : μ 1000
9 … A manufacturer claims that their light bulbs burn for an average of 1000 hours. We have reason to believe that the bulbs do not last that long. . .. If we reject the manufacturer’s claim, we must accept the alternate hypothesis that the light bulbs do not last as long as 1000 hours. H 1 : μ < 1000

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10 Types of Statistical Tests Left-tailed : H 1 states that the parameter is less than the value claimed in H 0 . Right-tailed : H 1 states that the parameter is greater than the value claimed in H 0 . Two-tailed : H 1 states that the parameter is different from ( ) the value claimed in H 0 .
11 Given the Null Hypothesis H 0 : μ k If you believe that is less than k , Use the left-tailed test: H 1 : < k

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12 If you believe that μ is more than k , Use the right-tailed test: H 1 : > k Given the Null Hypothesis H 0 : k
13 If you believe that μ is different from k , Use the two-tailed test: H 1 : k Given the Null Hypothesis H 0 : = k

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14 General Procedure for Hypothesis Testing Formulate the null and alternate hypotheses. Take a simple random sample. Compute a test statistic corresponding to the parameter in H 0 . Assess the compatibility of the test statistic with H 0 .
15 Hypothesis Testing about the Mean of a Normal Distribution with a Known Standard Deviation σ n / - x z statistic test σ μ = = size sample n H in stated value sample random simple of mean x 0 = = μ =

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16 P -value of a Statistical Test Assuming H 0 is true, the probability that the test statistic (computed from sample data) will take on values as extreme as or more than the observed test statistic is called the P -value of the test The smaller the P -value computed from sample data, the stronger the evidence against H 0 .
17 P -values for Testing a Mean Using the Standard Normal Distribution n / - x z statistic test sample ed standardiz the Use x σ μ = =

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18 P -value for a Left-tailed Test P -value = probability of getting a test statistic less than x z
19 P -value = probability of getting a test statistic greater than x z P -value for a Right-tailed Test

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## This note was uploaded on 10/19/2009 for the course MATH MATH300 taught by Professor Jones during the Spring '09 term at Northwood University, Michigan Campus.

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Hypothesis_Testing - Hypothesis Testing Hypothesis testing...

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