Week 91 Simple versus Composite Hypothesis Recall, a simple hypothesis completely specifies the distribution. A composite does not. When testing a simple.

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week 91 Simple versus Composite Hypothesis Recall, a simple hypothesis completely specifies the distribution. A composite does not. When testing a simple null hypothesis versus a composite alternative, the power of the test is a function of the parameter of interest. In addition, the power is also affected by the sample size.

week 92 Example

week 93 Test for Mean of Normal Population σ 2 is known Suppose X 1, …, X n is a random sample from a N(μ, σ 2 ) distribution where σ 2 is known. We are interested in testing hypotheses about μ. The test statistics is the standardized version of the sample mean. We could test three sets of hypotheses…

week 94 Test for Mean of Normal Population σ 2 is unknown Suppose X 1, …, X n is a random sample from a N(μ, σ 2 ) distribution where σ 2 is unknown, n is small and we are interested in testing hypotheses about μ. The test statistics is...

week 95 Example In a metropolitan area, the concentration of cadmium (Cd) in leaf lettuce was measured in 6 representative gardens where sewage sludge was used as fertilizer. The following measurements (in mg/kg of dry weight) were obtained. Cd: Is there evidence that the mean concentration of Cd is higher than 12.

week 96 Test for Mean of a Non-Normal Population Suppose X 1, …, X n are iid from some distribution with E(X i )=μ and Var(X i )= σ 2. Further suppose that n is large and we are interested in testing hypotheses about μ. Since n is large the CLT applies to the sample mean and the test statistics is again the standardized version of the sample mean.

week 97 Example –Binomial Distribution Suppose X 1,…,X n are random sample from Bernoulli(θ) distribution. We are interested in testing hypotheses about θ…