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6. (16 points) Let X₁,..., Xn d F and let µ = EF(X₁). We want to test Hoμ = 0 versus Η : μ = 0. (a) Assume the data are
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6. (16 points) Let X₁,..., Xn d F and let µ = EF(X₁). We want to test Hoμ = 0 versus Η : μ = 0. (a) Assume the data are
6. (16 points) Let X₁,..., Xn d F and let µ = EF(X₁). We want to test Hoμ = 0 versus Η : μ = 0. (a) Assume the data are drawn from a normal distribution, i.e., F = N(μ, o2), where o² is known. Find the most appropriate tests to use, respectively, when the sample size is large or small. Include a test statistic, how to find the rejectionfregion or p-value. (b) Repeat (a) but now assume that o2 is unknown. Find the most appropriate test. (c) Explain how to use the nonparametric bootstrap (for the standard error) to construct a Wald test without assuming normality. (d) Explain how to use the parametric bootstrap (for the standard error) to construct a Wald test assuming normality but o2 unknown.
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