2. Suppose that we have 9 independent observations from a normal distribution with standard deviation 10....
We are looking to calculate the power of a one-sided test from n independent observations from a N(μ, σ2) distribution with a null hypothesis of Ho : μ-μο and an alternative H1 : μ > μο. Supposing that we know σ2, we can form a test statistic o/Vn and reject the null hypothesis when T > 1.645. This test has level α = 0.05. We want a formula for the power of this test against the alternative that μ-A-This power...
2. Suppose that we have n independent observations x1, ,Tn from a normal distribution with mean μ and variance σ2, and we want to test (a) Find the maximum likelihood estimator of μ when the null hypothesis is true. (b) Calculate the Likelihood Ratio Test Statistic 7-2 log max L(μ, σ*) )-2 log ( max L(u, i) μισ (c) Explain as clearly as you can what happens to T, when our estimate of σ2 is less than 1. (d) Show...
2. Suppose that we have n independent observations x1,..., xn from a normal distribution with mean μ and variance σ, and we want to test (a) Find the maximum likelihood estimator of μ when the null hypothesis is true. (b) Calculate the Likelihood Ratio Test Statistic 2 lo g max L(μ, σ log | max L( 1) (c) Explain as clearly as you can what happens to T when our estimate of σ2 is less than 1. (d) Show that...
2. Suppose that we have n independent observations x1,..., xn from a normal distribution with mean μ and variance σ, and we want to test (a) Find the maximum likelihood estimator of μ when the null hypothesis is true. (b) Calculate the Likelihood Ratio Test Statistic 2 lo g max L(μ, σ log | max L( 1) (c) Explain as clearly as you can what happens to T when our estimate of σ2 is less than 1. (d) Show that...
We are looking to calculate the power of a one-sided test from n independent observations Xi from a N(μ, σ2) distribution with a null hypothesis of Ho : μ-μ0 and an alternative H, : μ 〉 μ0. Supposing that we know σ2, we can form a test statistic T= and reject the null hypothesis when T 〉 1.645. This test has level α 0.05. We want a formula for the power of this test against the alternative that μ-74-This power...
We are looking to calculate the power of a one-sided test from n independent observations xi from a N (µ, σ2 ) distribution with a null hypothesis of H0 : µ = µ0 and an alternative H1 : µ > µ0. Supposing that we know σ2, we can form a test statistic T = (x¯ − µ0)/(σ/√n) and reject the null hypothesis when T > 1.645. This test has level α = 0.05. We want a formula for the power...
Use R to find to find the answers to the problems 2. (25 points) Suppose that we have a sample of size n 64, we know the population standard deviation is σ 48, and we are considering a normally distributed population, we want to test the hypotheses: Ho : μ-200 Hi 200 We are going to use a z-test because σ is known. We will use a significance level of:-0.05. (a) What is the critica z value? In other words,...
2. Hypothesis tests about a population mean, population standard deviation known Aa Aa Lenders tighten or loosen their standards for issuing credit as economic conditions change. One of the criteria lenders use to evaluate the creditworthiness of a potential borrower is her credit risk score, usually a FICO score. FICO scores range from 300 to 850. A consumer with a high FICO score is perceived to be a low credit risk to the lender and is more likely to be...