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Ch 4 Stat inferences

Ch 4 Stat inferences - INDE 321 Quality Control Instructor...

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INDE 321: Quality Control Instructor : Linda Boyle, University of Washington Dept. of Industrial and Systems Engineering Dept. of Civil and Environmental Engineering Chapter 4 Statistical inferences

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Chapter 4: Inferences about Process Quality In real life, we infer something about the population using a random sample Descriptive statistics describe the sample Sampling distributions describe the distribution of a sample . useful for hypothesis testing and parameter estimations.
Sampling Distributions Sampling from a Normal Distribution Chi-square ( χ 2 ) distribution t distribution F distribution Sampling from Bernoulli Distribution The sum sum of a sample from a Bernoulli process has a binomial distribution Sampling from Poisson Distribution

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Chapter 4 Two categories of statistical inferences: 1. Parameter Estimation 2. Hypothesis Testing
Parameter Estimation Parameters are values representing the population. e.g., μ , σ 2 (The population mean and variance, respectively). Parameters in reality are often unknown and must be estimated. Statistics are estimates of parameters. e.g., (The sample mean and variance, respectively). 2 S , x

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Hypothesis Testing A statistical hypothesis is a statement about the parameters of a probability distribution. Single Sample Null hypothesis Alternative hypothesis 0 1 0 0 : H : H μ μ μ = μ
Statistical Inference (Single Sample) Example: An automobile manufacturer claims a particular automobile can average 35 mpg (highway). Suppose we are interested in testing this claim. We will sample 25 cars under identical conditions and calculate average mpg for sample. Before data collection, decide the following if sample average is less than 33 mpg or more than 37 mpg we will reject the makers claim (critical values)

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Statistical Inference (Single Sample) Example (continued) H 0 : μ = 35 H 1 : μ ≠ 35 From the sample of 25 cars, the average mpg was found to be 31.5 . What is your conclusion?
Statistical Inference - Definitions Significance Level The level of significance , α determines the size of the rejection region. It is also known as the probability of a “Type I error” (want this to be small) Type I error - rejecting the null hypothesis when it is true. How small? Usually want 10 . 0 or 05 . 0 α α

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Statistical Inference - Definitions Types of Error Type I error - rejecting the null hypothesis when it is true. Pr(Type I error) = α . Sometimes called the producer’s risk . Probability that a good lot will be rejected Type II error - not rejecting the null hypothesis when it is false. Pr(Type II error) = β . Sometimes called the consumer’s risk . Probability that a poor lot will continue out the door
Statistical Inference - Definitions Power of a Test The Power of a test of hypothesis is given by 1 - β That is, 1 - β is the probability of: correctly rejecting the null hypothesis, or rejecting the null hypothesis when the alternative is true.

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Statistical Hypothesis
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Ch 4 Stat inferences - INDE 321 Quality Control Instructor...

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