Hypothesis_Testing_t_testing_lecture

Hypothesis_Testing_t_testing_lecture - Hypothesis Testing,...

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Hypothesis Testing, σ Unknown Case I: 1. The population has any distribution 2. The sample size is large (n 30) 3. σ is unknown. Since n is large, the value of σ is approximated by the sample standard deviation s. _ Χ - μ z = ------------- s n Case II: 1. The population is normally distributed 2. The sample size n is small. 3. σ is unknown. USE t-test __ Χ - μ t = ------------ s n degree of freedom ν = n – 1 Use Table 5 t-distribution table Example: 1. 2-tailed test, α = 0.05, ν = 6 t c = 2.447 2. 2-tailed test, α = 0.01, ν = 12 t c = 3.055 3. one-tailed test, α = 0.05, ν = 7 t c = 1.895 4. one-tailed test, α = 0.01, ν = 11 t c = 2.718 t c critical t value
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Hypothesis testing, σ unknown Examples: 1. Experience has shown that the number of matches in boxes follow a normal distribution. A manufacturer claims that the average number of matches in its boxes is 50. A customer purchases a random sample of 9 boxes and counts the contents of each box. They were: 49 50 51 46 48 45 52 47 48 Based on this sample, should the customer believe the manufacturer’s claim? Use 2-tailed test, α = 0.05. μ = 50 μ is the standard mean, the one that we want to test. n = 9, so ν = n – 1 = 8 s = calculate standard deviation of the sample data = use s x of your Sharp calculator or σ n-1 of your Casio calculator. s = 2.29 X (mean) = 48.4 H 0 : μ = 50 H 1 : μ 50 this makes our test 2-tailed α = 0.05, ν = 8 t c = 2.306 our computed t value should be within range –2.306 t 2.306 Χ - μ 48.4 - 50 t = ------------ = --------------- = -2.03 s 2.29 n 9 Since –2.03 is within the range –2.306 t 2.306, retain H 0 Therefore, the number of matches per box remains at 50.
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2. The number of errors on the pages of a statistics textbook follows a normal
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Hypothesis_Testing_t_testing_lecture - Hypothesis Testing,...

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