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ES04 - Coggle Diagram

- - - - To estimate a parameter, sample statistics will be used (point estimator); once the sample is selected, a numerical value of the statistic is given (point estimate)
        
        Important Questions
        
        Which point estimator to choose?
        
        How to compare unbiased estimators?
        
        MVUE
        
        e.g. the sample median, the sample mean, and a single observation are all unbiased estimator
        
        How to compare estimators?
        
        Relative Efficiency
        
        e.g. the relative efficiency of a single observation to the sample mean is less than 1, so the sample mean is a better estimator
        
        How do we compare biased estimators?
        
        MSE
        
        e.g. the sample std. dev. is a biased estimator of the population std. dev.
        
        How precise is our estimation?
        
        Standard Error and Estimated Standard Error
  - - - Design and engineering specifications, to verify a theory, to determine if a process has changed
    - - A statement about the parameters of one or more population is made (a statistical hypothesis). To test it, a random sample from the population is taken. A test statistic is computed and if the information in the sample is consistent with our hypothesis, we conclude it is true
        
        Important Questions
        
        How do we (dis)prove the hypothesis?
        
        We can't, unless we examine the entire population. We can only infer. So there's the possibility that our conclusion is incorrect
        
        What if our conclusion is incorrect?
        
        Type I Error (α)
        
        rejecting the null hypothesis when it's true
        
        Type II Error (β)
        
        failing to reject the null hypothesis when it's false
        
        Which hypothesis can we formulate?
        
        Infer on the population variance
        
        Infer on the population proportion
        
        Infer on the population mean
        
        If σ is known, then we use the z-test
        
        If σ is unknown, and the sample is small: we assume the distribution is normal and use the t-test
        
        If σ is unknown, and the sample is large (n≳40): s≅σ and we can use the z-test regardless of the population distribution
        
        If σ is unknown, and the sample size is small, and the normal distribution assumption is unreasonable, we use different techniques
  - - - We are often interested in finding an interval in which we would expect to find the true value of a parameter