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6. Suppose we observe Y,... Yn from a normal distribution with unknown parameters such that Y...
6. Suppose we obeerve Yi,...Yn from a normal distribution with unknown parameters such that Y 24,...
6. Suppose we obeerve Yi,...Yn from a normal distribution with unknown parameters such that Y 24, 236, and (a) Find the rejection region of a level a-0.05 test of Ho : μ-20 vs. Hi :"t 20. Would this test reject with the (b) Find the rejection region of a level α-0.05 test of Ho : μ 20 vs. H: μ > 20, would this test reject with the given data? given data? (c) Will the p-value for the given data...
6 and 7 6. Suppose we observe Y...Yn from a normal distribution with alaiuctess n 15...
6 and 7
6. Suppose we observe Y...Yn from a normal distribution with alaiuctess n 15 (a) Find the rejection region of a level a 0.05 test of Ho 20 vs. H20. Would this test reject with the given data? (b) Find the rejection region of a level a-0.05 test of H0 : 20 vs. Hi : > 20. Would this test reject with the given data? (c) Will the p-value for the given data be smaller in part (a)...
5. Suppose we observe Y Yn from a normal distribution with unknown parameters such that '...
5. Suppose we observe Y Yn from a normal distribution with unknown parameters such that ' 20, s2 = 16, and n= 10. (a) Find a 95% confidence interval for (b) Now suppose n-1000, with the sarne value of P and 8. Find a 95% confidence interval for μ. (c) Would your answer to (a) or (b) change if the data were not from a normal distribution?
A random sample of 16 values is drawn from a mound-shaped and symmetric distribution. The sample...
A random sample of 16 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 9 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 8.5. (a) Is it appropriate to use a Student's t distribution? Explain. Yes, because the x distribution is mound-shaped and symmetric and σ is unknown. No, the x distribution is skewed left. No, the...
Suppose that the underlying distribution is approximately normal but with unknown variance. You would like to...
Suppose that the underlying distribution is approximately normal but with unknown variance. You would like to test H0 : μ = 50 vs. H1 : μ < 50. Calculate the p-value for the following 6 observations: 48.9, 50.1, 46.4, 47.2, 50.7, 48.0. O less than 0.01 O between 0.01 and 0.025 O between 0.025 and 0.05 between 0.05 and 0.1 O more than 0.1
A random sample of 16 values is drawn from a mound-shaped and symmetric distribution. The sample...
A random sample of 16 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 15 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 14.5. (a) Is it appropriate to use a Student's t distribution? Explain. Yes, because the x distribution is mound-shaped and symmetric and σ is unknown.No, the x distribution is skewed left. No, the x distribution...
Suppose that X1,X2, ,Xn are iid N(μ, σ2), where both parameters are unknown. Derive the likelihood...
Suppose that X1,X2, ,Xn are iid N(μ, σ2), where both parameters are unknown. Derive the likelihood ratio test (LRT) of Ho : σ2 < σ1 versus Ho : σ2 > σ.. (a) Argue that a LRT will reject Ho when w(x)S2 2 0 is large and find the critical value to confer a size α test. (b) Derive the power function of the LRT
5. Suppose we obaerve Y. ..Y, from a normal distribution with unknown parameters such that P...
5. Suppose we obaerve Y. ..Y, from a normal distribution with unknown parameters such that P - 20, s n=10. 16, and (a) Find a 95% confidence interval for (b) Now suppose n-1000, with the same value of Y and s. Find a 95% confidence interval for G) Would your answer to (a) or (b) change if the data were not from a normal distribution?
Now consider the above problem in a different way: Assume that X is following a normal...
Now consider the above problem in a different way: Assume that X is following a normal distribution with mean u and known variance σ2 4. We want to test H0 : μ 1 vs. H1 : μ-2 based on a sample of size n. The decision rule is to reject Ho if R Find n and c such that α 0.05 and β = 0.05. c.
A sample of size 36 is taken from a population with unknown mean and standard deviation...
A sample of size 36 is taken from a population with unknown mean and standard deviation 4.5. In a test of H0: μ = 5 vs. Ha: μ < 5, if the sample mean was 4, which of the following is true? (i) We would reject the null hypothesis at α = 0.01. (ii) We would reject the null hypothesis at α = 0.05. (iii) We would reject the null hypothesis at α = 0.10.
6. Suppose we obeerve Yi,...Yn from a normal distribution with unknown parameters such that Y 24, 236, and (a) Find the rejection region of a level a-0.05 test of Ho : μ-20 vs. Hi :"t 20. Would this test reject with the (b) Find the rejection region of a level α-0.05 test of Ho : μ 20 vs. H: μ > 20, would this test reject with the given data? given data? (c) Will the p-value for the given data...
6 and 7
6. Suppose we observe Y...Yn from a normal distribution with alaiuctess n 15 (a) Find the rejection region of a level a 0.05 test of Ho 20 vs. H20. Would this test reject with the given data? (b) Find the rejection region of a level a-0.05 test of H0 : 20 vs. Hi : > 20. Would this test reject with the given data? (c) Will the p-value for the given data be smaller in part (a)...
5. Suppose we observe Y Yn from a normal distribution with unknown parameters such that ' 20, s2 = 16, and n= 10. (a) Find a 95% confidence interval for (b) Now suppose n-1000, with the sarne value of P and 8. Find a 95% confidence interval for μ. (c) Would your answer to (a) or (b) change if the data were not from a normal distribution?
Suppose that the underlying distribution is approximately normal but with unknown variance. You would like to test H0 : μ = 50 vs. H1 : μ < 50. Calculate the p-value for the following 6 observations: 48.9, 50.1, 46.4, 47.2, 50.7, 48.0. O less than 0.01 O between 0.01 and 0.025 O between 0.025 and 0.05 between 0.05 and 0.1 O more than 0.1
Suppose that X1,X2, ,Xn are iid N(μ, σ2), where both parameters are unknown. Derive the likelihood ratio test (LRT) of Ho : σ2 < σ1 versus Ho : σ2 > σ.. (a) Argue that a LRT will reject Ho when w(x)S2 2 0 is large and find the critical value to confer a size α test. (b) Derive the power function of the LRT
5. Suppose we obaerve Y. ..Y, from a normal distribution with unknown parameters such that P - 20, s n=10. 16, and (a) Find a 95% confidence interval for (b) Now suppose n-1000, with the same value of Y and s. Find a 95% confidence interval for G) Would your answer to (a) or (b) change if the data were not from a normal distribution?
Now consider the above problem in a different way: Assume that X is following a normal distribution with mean u and known variance σ2 4. We want to test H0 : μ 1 vs. H1 : μ-2 based on a sample of size n. The decision rule is to reject Ho if R Find n and c such that α 0.05 and β = 0.05. c.
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