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2. We wish to perform a.05 level test based on a single piece of data. The...
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...
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...
2. Perform the following .05 level test: Ho: 6 = 2.5 vs. Ha: 0 < 2.5,...
2. Perform the following .05 level test: Ho: 6 = 2.5 vs. Ha: 0 < 2.5, given a random sample of 10 pieces of data had a mean of 13.6 and a standard deviation of 1.7. Ho: Test Statistic: Ha: p-value: Conclusion (Circle Answer): Fail to Reject Ho R eject Ho
Suppose that we wish to test the null hypothesis Ho that the proportion p of ledger...
Suppose that we wish to test the null hypothesis Ho that the proportion p of ledger sheets with errors is equal to .05 versus the alternative Ha , that the proportion is larger than .05, by using the following scheme. Two ledger sheets are selected at random. If both are error free, we reject Ho. If one or more contains an error, we look at a third sheet. If the third sheet is error free, we reject Ho. In all...
07 (15) Suppose that we wish to test the null hypothesis Ho that the proportion p...
07 (15) Suppose that we wish to test the null hypothesis Ho that the proportion p of ledger sheets with errors is equal to .05 versus the alternative Ha , that the proportion is larger than .05, by using the following scheme. Two ledger sheets are selected at random. If both are error free, we reject Ho. If one or more contains an error, we look at a third sheet. If the third sheet is error free, we reject Ho....
We wish to test H0: = 0 versus Ha: > 0. If we calculate a test statistic of =...
We wish to test H0: = 0 versus Ha: > 0. If we calculate a test statistic of = 0.6, then my p-value will be closest to 0.003 0.300 0.600 0.950 When estimating , the proportion of voting age citizens who will vote for Candidate A, political researchers calculate the 90% confidence interval (0.67, 0.73). If we were to also test the hypotheses H0: = 0.666 versus Ha: 0.666 using a significance level of = 0.10, we would decide to accept H0. reject H0. not reject...
3. Let X,,X,,..., X, be a random sample from a Gamma 40distribution, where 6>0. we wish to test H0 : θ-1 vs. Hi : θ #1. Show that the likelihood ratio test statistic, A , can be written as A(V) wh...
3. Let X,,X,,..., X, be a random sample from a Gamma 40distribution, where 6>0. we wish to test H0 : θ-1 vs. Hi : θ #1. Show that the likelihood ratio test statistic, A , can be written as A(V) where a. What is the distribution of V? what is the null distribution of what will be the rejection region for an α level test? b. 20 d.
3. Let X,,X,,..., X, be a random sample from a Gamma 40distribution,...
5. Suppose X a single observation from a population with a Beta(0,1) distribution. (a) Suppose we...
5. Suppose X a single observation from a population with a Beta(0,1) distribution. (a) Suppose we want to test Ho :0 <1 against H :0>1 an we use a rejection region of X > 1/2. Find the size and power function for this test. Sketch the power function. (b) Now suppose we want to test H, :0 = 1 against H :0 = 2. Find the most powerful level a test. (Is there a Theorem we can use?) (C) Is...
3. Suppose that we are testing Ho: u = 80 vs. Ha: u <80 at the...
3. Suppose that we are testing Ho: u = 80 vs. Ha: u <80 at the .05 level and we are going to collect 10 pieces of data and o=1.2. Determine the probability of Type Il error for the alternative kl. = 79.25. ANSWER 4. Company A claims that their tires outlast the tires of Company B by more than 12.000 miles. We feel certain that Il = 62,000 ,- 5,100. Data for Company A is collected and summarized: Company...
K=42,n=1,m=18 8. The amount of time it takes a student to solve a homework problem in mathematical statistics (in minutes) follows a normal distribution with unknown mean μ and a variance equal to...
K=42,n=1,m=18
8. The amount of time it takes a student to solve a homework problem in mathematical statistics (in minutes) follows a normal distribution with unknown mean μ and a variance equal to 9m2. Find the most powerful test to verify the null hypothesis that μ k against the alternative that , 2k on the base of k independent observations, for a significance level of n%. Calculate the power of this test (for the alternative hypothesis). What is the decision,...
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...
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...
2. Perform the following .05 level test: Ho: 6 = 2.5 vs. Ha: 0 < 2.5, given a random sample of 10 pieces of data had a mean of 13.6 and a standard deviation of 1.7. Ho: Test Statistic: Ha: p-value: Conclusion (Circle Answer): Fail to Reject Ho R eject Ho
Suppose that we wish to test the null hypothesis Ho that the proportion p of ledger sheets with errors is equal to .05 versus the alternative Ha , that the proportion is larger than .05, by using the following scheme. Two ledger sheets are selected at random. If both are error free, we reject Ho. If one or more contains an error, we look at a third sheet. If the third sheet is error free, we reject Ho. In all...
07 (15) Suppose that we wish to test the null hypothesis Ho that the proportion p of ledger sheets with errors is equal to .05 versus the alternative Ha , that the proportion is larger than .05, by using the following scheme. Two ledger sheets are selected at random. If both are error free, we reject Ho. If one or more contains an error, we look at a third sheet. If the third sheet is error free, we reject Ho....
3. Let X,,X,,..., X, be a random sample from a Gamma 40distribution, where 6>0. we wish to test H0 : θ-1 vs. Hi : θ #1. Show that the likelihood ratio test statistic, A , can be written as A(V) where a. What is the distribution of V? what is the null distribution of what will be the rejection region for an α level test? b. 20 d.
3. Let X,,X,,..., X, be a random sample from a Gamma 40distribution,...
5. Suppose X a single observation from a population with a Beta(0,1) distribution. (a) Suppose we want to test Ho :0 <1 against H :0>1 an we use a rejection region of X > 1/2. Find the size and power function for this test. Sketch the power function. (b) Now suppose we want to test H, :0 = 1 against H :0 = 2. Find the most powerful level a test. (Is there a Theorem we can use?) (C) Is...
3. Suppose that we are testing Ho: u = 80 vs. Ha: u <80 at the .05 level and we are going to collect 10 pieces of data and o=1.2. Determine the probability of Type Il error for the alternative kl. = 79.25. ANSWER 4. Company A claims that their tires outlast the tires of Company B by more than 12.000 miles. We feel certain that Il = 62,000 ,- 5,100. Data for Company A is collected and summarized: Company...
K=42,n=1,m=18
8. The amount of time it takes a student to solve a homework problem in mathematical statistics (in minutes) follows a normal distribution with unknown mean μ and a variance equal to 9m2. Find the most powerful test to verify the null hypothesis that μ k against the alternative that , 2k on the base of k independent observations, for a significance level of n%. Calculate the power of this test (for the alternative hypothesis). What is the decision,...
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