Consider a random sample from N(u, 0.1082), and the null hypothesis Ho : u = 4.55....

Transcribed Image Text:

Consider a random sample from N(u, 0.1082), and the null hypothesis Ho : u = 4.55. Suppose we observed a set of data with n = 9, = 4.484. 1. Let H1 : µ + 4.55, the p-value of the observed = 4.484 is (Please round to 2 significant figures.) 2. Let H1 : u < 4.55, the p-value of the observed a 4.484 is (Please round to 2 significant figures.) Consider a normal random sample from population N (u, o?), where o2 is assumed to be known. Consider the following hypotheses: Hρ : μ. μο υ. s. Η1 : μ-μι μο Let the rejection region be { : < Ho - Zao/Vn},then the type-ll error is β= P(X >μο- 2α/νη | μ = μ). 1. For a fixed sample size n, when a decreases, B will (Type in "O" if you think it will decrease, and "1" if you think it will increase.) 2. For a fixed sample size n, when Bincreases, a will (Type in "O" if you think it will decrease, and "1" if you think it will increase.) 3. Let σ- 0.12, μι = lo – 0.03, a minimum number of samples are needed if we want to ensure that a < 0.025, B < 0.025. (Hint: round UP to the nearest integer.) Consider a random sample from N(u, 0.1082), and the null hypothesis Ho : u = 4.55. Suppose we observed a set of data with n = 9, = 4.484. 1. Let H1 : µ + 4.55, the p-value of the observed = 4.484 is (Please round to 2 significant figures.) 2. Let H1 : u < 4.55, the p-value of the observed a 4.484 is (Please round to 2 significant figures.) Consider a normal random sample from population N (u, o?), where o2 is assumed to be known. Consider the following hypotheses: Hρ : μ. μο υ. s. Η1 : μ-μι μο Let the rejection region be { : < Ho - Zao/Vn},then the type-ll error is β= P(X >μο- 2α/νη | μ = μ). 1. For a fixed sample size n, when a decreases, B will (Type in "O" if you think it will decrease, and "1" if you think it will increase.) 2. For a fixed sample size n, when Bincreases, a will (Type in "O" if you think it will decrease, and "1" if you think it will increase.) 3. Let σ- 0.12, μι = lo – 0.03, a minimum number of samples are needed if we want to ensure that a < 0.025, B < 0.025. (Hint: round UP to the nearest integer.)