Math Problem Statement
STAT 432 PROBLEMSET 4a (2).pdf
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Solution
The document contains a series of hypothesis testing problems involving the Generalized Likelihood Ratio (GLR) tests, specifically focused on various distributions (e.g., normal, exponential, Poisson, and Weibull). Here’s a quick breakdown of a few selected problems to illustrate the types of tasks:
- Problem 1: Derive a GLR test of size for testing vs using a normal distribution with unknown mean .
- Problem 3: Demonstrate that the GLR test for vs for an exponential distribution has a critical region and explore its modification for chi-square table application.
- Problem 5 (b): For a given sample size and observed mean, determine if is accepted at .
- Problem 11: Apply the GLR test on a sample of waiting times to evaluate if the true mean is different from a hypothesized value.
Would you like a solution for a specific problem, or a general explanation of GLR test derivation?
Related Questions
- How is the GLR test derived for normal distributions with unknown mean and variance?
- What adjustments are necessary for using chi-square tables with exponential distributions in hypothesis testing?
- How can you interpret the critical region in hypothesis testing?
- What are the implications of sample size on the acceptance of at a specified significance level?
- How is the likelihood ratio principle applied in tests involving non-standard distributions?
Tip
To solve these types of problems, start by writing down the likelihood function and then derive the likelihood ratio.
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Math Problem Analysis
Mathematical Concepts
Generalized Likelihood Ratio (GLR) tests
Hypothesis testing
Normal distribution
Exponential distribution
Poisson distribution
Weibull distribution
Formulas
GLR test statistic
Likelihood function
Critical region determination
Theorems
Likelihood ratio principle
Chi-square distribution for critical region adjustment
Suitable Grade Level
Undergraduate
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