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(b) Find the pr Problem 2. Let x,, ,X, be We wish to test Ho versus...
N(0,02). We wish to use a 1. [18 marks] Suppose X hypothesis single value X = x to test the null Ho : 0 = 1 against the...
N(0,02). We wish to use a 1. [18 marks] Suppose X hypothesis single value X = x to test the null Ho : 0 = 1 against the alternative hypothesis H1 0 2 Denote by C aat the critical region of a test at the significance level of : α-0.05. (f [2 marks] Show that the test is also the uniformly most powerful (UMP) test when the alternative hypothesis is replaced with H1 0 > 1 (g) [2 marks Show...
4-116 Suppose we wish to test the hypothesi s Ho: u WILEY versus the alternative : > 85 where T-1...
4-116 Suppose we wish to test the hypothesi s Ho: u WILEY versus the alternative : > 85 where T-16. Suppose that the true mean is μ 86 and that in the practical context of the -85 that has practical problem this is not a departure from μ0 significance (a) For a test with α 0.01, compute β for the sample sizes n-25, 100, 400, and 2500 assuming that μ-86 (b) Suppose the sample average is x - 86. Find...
18 marks] Suppose X~N(0,0). We wish to use a single value X hypothesis to test the null against the alternative hypothe...
18 marks] Suppose X~N(0,0). We wish to use a single value X hypothesis to test the null against the alternative hypothesis Denote by C aa) the critical region of a test at the significance level of -0.05 (a) 2 marks] What is the sample space S, the parameter space 9 space Θο of the test? and the null parameter (b) 12 marks) Computea (c) 12 marks Compute the power of the test (i.e., at 2) (d) [2 marks] Compute the...
7. Suppose X,Y "Unif( 0, 0+1). Suppose the scientists wish to test Ho : 0 =...
7. Suppose X,Y "Unif( 0, 0+1). Suppose the scientists wish to test Ho : 0 = 0 versus H: >0. Suppose we have two possible test procedures that we wish to compare: Decision rule for test procedure 1: Reject Ho in favor of H, if Y>0.95. Decision rule for test procedure 2: Reject Ho in favor of H, if X+Y > d. Find the value of d for which the second of these test procedures has the same significance level...
5. Let X ~ N( ,o2) and assume ơ--3. We are to test the null hypothesis Ho: 10 against e) Let a -0...
5. Let X ~ N( ,o2) and assume ơ--3. We are to test the null hypothesis Ho: 10 against e) Let a -0.05. Design a test to accept or reject He (b) Determine and the power of your test. (c) Plot the probability density functions under the two hypotheses in the same coordinate systern and locate the critical value, acceptance and critical regions, and designate the quantities α and β graphically. revised hypothesis we have β 0.05. Then do (c)...
help please !! To test Ho: 0 = 2.3 versus H: > 2.3, a random sample...
help please !!
To test Ho: 0 = 2.3 versus H: > 2.3, a random sample of size n=20 is obtained from a population that is known to be normally distributed. (a) If the sample standard deviation is determined to be s 3.1. compute the test statistic (b) of the researcher decides to test this hypothesis at the a= 0.05 level of significance, use technology to determine the P-value. (c) Will the researcher reject the null hypothesis? (a) The test...
In a test of the hypothesis Ho: u = 59 versus Ha: u>59, a sample of...
In a test of the hypothesis Ho: u = 59 versus Ha: u>59, a sample of n = 100 observations possessed mean x = 58.5 and standard deviation s = 3.8. Find and interpret the p-value for this test. The p-value for this test is (Round to three decimal places as needed.)
You wish to test the claim that μ ≠ 22 at a level of significance of α = 0.05 and are given sample statistics n = 35, x...
You wish to test the claim that μ ≠ 22 at a level of significance of α = 0.05 and are given sample statistics n = 35, x = 21.1, and s = 2.7. Compute the value of the standardized test statistic. Round your answer to two decimal places. a)Ho:___Ha:___
We wish to test H0:1p = 0.30 vs. H1: p > 0.30, where p is the...
We wish to test H0:1p = 0.30 vs. H1: p > 0.30, where p is the proportion of students who want to attend the game. Let X be the number of individuals in a random sample of n = 25 students who want to attend the game. a) As the sample size n increases, the power of the test also increases. Consider n = 150. For the rejection region "Reject Ho if X >= 53", find ... (i) the significance...
You wish to test Hou = 63.5 versus Hoiu + 63.5 at a significance level of...
You wish to test Hou = 63.5 versus Hoiu + 63.5 at a significance level of 0.05. You obtain a sample of size 26 with a mean of 66.5 and a standard deviation of 19.4. You believe that the population is normally distributed. ROUND YOUR ANSWERS TO THREE DECIMAL PLACES. (a). What is the test statistic? Do not round your interim calculations. (b). Using your answer from part (a), find the p-value: (c). What is the positive critical value for...
N(0,02). We wish to use a 1. [18 marks] Suppose X hypothesis single value X = x to test the null Ho : 0 = 1 against the alternative hypothesis H1 0 2 Denote by C aat the critical region of a test at the significance level of : α-0.05. (f [2 marks] Show that the test is also the uniformly most powerful (UMP) test when the alternative hypothesis is replaced with H1 0 > 1 (g) [2 marks Show...
4-116 Suppose we wish to test the hypothesi s Ho: u WILEY versus the alternative : > 85 where T-16. Suppose that the true mean is μ 86 and that in the practical context of the -85 that has practical problem this is not a departure from μ0 significance (a) For a test with α 0.01, compute β for the sample sizes n-25, 100, 400, and 2500 assuming that μ-86 (b) Suppose the sample average is x - 86. Find...
18 marks] Suppose X~N(0,0). We wish to use a single value X hypothesis to test the null against the alternative hypothesis Denote by C aa) the critical region of a test at the significance level of -0.05 (a) 2 marks] What is the sample space S, the parameter space 9 space Θο of the test? and the null parameter (b) 12 marks) Computea (c) 12 marks Compute the power of the test (i.e., at 2) (d) [2 marks] Compute the...
7. Suppose X,Y "Unif( 0, 0+1). Suppose the scientists wish to test Ho : 0 = 0 versus H: >0. Suppose we have two possible test procedures that we wish to compare: Decision rule for test procedure 1: Reject Ho in favor of H, if Y>0.95. Decision rule for test procedure 2: Reject Ho in favor of H, if X+Y > d. Find the value of d for which the second of these test procedures has the same significance level...
5. Let X ~ N( ,o2) and assume ơ--3. We are to test the null hypothesis Ho: 10 against e) Let a -0.05. Design a test to accept or reject He (b) Determine and the power of your test. (c) Plot the probability density functions under the two hypotheses in the same coordinate systern and locate the critical value, acceptance and critical regions, and designate the quantities α and β graphically. revised hypothesis we have β 0.05. Then do (c)...
help please !!
To test Ho: 0 = 2.3 versus H: > 2.3, a random sample of size n=20 is obtained from a population that is known to be normally distributed. (a) If the sample standard deviation is determined to be s 3.1. compute the test statistic (b) of the researcher decides to test this hypothesis at the a= 0.05 level of significance, use technology to determine the P-value. (c) Will the researcher reject the null hypothesis? (a) The test...
In a test of the hypothesis Ho: u = 59 versus Ha: u>59, a sample of n = 100 observations possessed mean x = 58.5 and standard deviation s = 3.8. Find and interpret the p-value for this test. The p-value for this test is (Round to three decimal places as needed.)
We wish to test H0:1p = 0.30 vs. H1: p > 0.30, where p is the proportion of students who want to attend the game. Let X be the number of individuals in a random sample of n = 25 students who want to attend the game. a) As the sample size n increases, the power of the test also increases. Consider n = 150. For the rejection region "Reject Ho if X >= 53", find ... (i) the significance...
You wish to test Hou = 63.5 versus Hoiu + 63.5 at a significance level of 0.05. You obtain a sample of size 26 with a mean of 66.5 and a standard deviation of 19.4. You believe that the population is normally distributed. ROUND YOUR ANSWERS TO THREE DECIMAL PLACES. (a). What is the test statistic? Do not round your interim calculations. (b). Using your answer from part (a), find the p-value: (c). What is the positive critical value for...
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