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(d) to 2.80 6. Suppose that you are testing the following hypothe ses where the variance...
1. Suppose that we are testing Hor = po versus H : > Ho with a...
1. Suppose that we are testing Hor = po versus H : > Ho with a sample size of n = 15. Calculate bounds on the P-value for the following observed values of the test statistic: (a) to = 2.35 (b) to = 3.55 (c) to = 1.55
2.11. Suppose that we are testing Ho: μ-μ0 versus H: >o with a sample size of...
2.11. Suppose that we are testing Ho: μ-μ0 versus H: >o with a sample size of n 15. Calculate bounds on the P-value for the following observed values of the test statistic: (a) to 2.35 (b)o 3.55 (c) 2.00 (d) to 1.55
Please solve 2.7, 2.8 and 2.9 problems. 2.7. Suppose that we are testing Ho : μ1...
Please solve 2.7, 2.8 and 2.9 problems.
2.7. Suppose that we are testing Ho : μ1 Ha versus Ho: > μ2 where the two sample sizes are ni n, 10. Both sample variances are unknown but assumed equal. Find bounds on the P-value for the following observed values of the test statistic. (a) to= 2.31 (b) toー3.60 (c) to-1.95 (d) 0-219 2.8. Consider the following sample data: 9.37, 13.04, 11.69, 8.21, 11.18, 10.41, 13.15, 11.51, 13.21, and 7.75. Is it...
Suppose that we are testing H 0 : μ 1 = μ 2 versus H 0...
Suppose that we are testing H 0 : μ 1 = μ 2 versus H 0 : μ 1 > μ 2 where the two sample sizes are n 1 = n 2 = 10 . Both sample variances are unknown but assumed equal. Find bounds on the P-value for the following observed values of the test statistic. t0=2.31 t0=3.60 t0=1.95 t0=2.19 Please do it by hand and show tables if they are used. Be detailed
Q4). Suppose that you are drawing a sample of random observations yyy2y, from a population that is normally distributed with a mean- u and variance 2. Derive the two-sided likelihood ratio test f...
Q4). Suppose that you are drawing a sample of random observations yyy2y, from a population that is normally distributed with a mean- u and variance 2. Derive the two-sided likelihood ratio test for testing Ho : μ Ho versus H! : μ where μ. μο. 123. (5 points)
Q4). Suppose that you are drawing a sample of random observations yyy2y, from a population that is normally distributed with a mean- u and variance 2. Derive the two-sided likelihood ratio test...
Question 21 In testing Ho: p1" p,-0 versus Ha: p1" p. 0, the computed value of...
Question 21 In testing Ho: p1" p,-0 versus Ha: p1" p. 0, the computed value of the test statistic is z = 2 25 The P value for this two-tailed test is then Not yet answered Points out of 6.00 Flag question Question 22 Not yet answered Points out of 4.00 The two-sample t test is applicable in situations in which population distributions are both normal when population variances have unknown values, and at least one of the two sample...
Exercises 10.3. Let Xi . . . , x N μ, σ2), whereơ2 s known to be equal to 100. In testing Ho : 25...
Exercises 10.3. Let Xi . . . , x N μ, σ2), whereơ2 s known to be equal to 100. In testing Ho : 25vs. H :H>25,h What sample size n would be necessary if one wishes to reject Ho with probability at least 95 if μ 26? iid se that a coin is to be tossed n times, and you wish to test the hypothesis Ho:p-12 VS. Hi P> I/2 at a- .05. What sample size n would be...
Suppose X1, .., Xn is a random sample from a N(0, a2) population, where variance o...
Suppose X1, .., Xn is a random sample from a N(0, a2) population, where variance o are known. Consider testing Ho : 0 = O0 vs. Hi 0 700 Q1(4pt): Using Likelihood Ratio Test (LRT) to obtain a level a test that rejects Ho if Уп(X — во) VП(х — во) <21-a/2 21-a/2 or о Q2(1pt): Is the two-sided test derived in 1) an uniformly most powerful test? If not, briefly state your reasons Q3 (1pt): Note that the test...
A sample from a Normal distribution with an unknown mean u and known variance o =...
A sample from a Normal distribution with an unknown mean u and known variance o = 45 was taken with n=9 samples giving sample mean of y = 3.6. (a) Construct a Hypothesis test with significance level a = 0.05 to test whether the mean is equal to 0 or it is greater than 0. What can you conclude based on the outcome of the sample? (b) Calculate the power of this test if the true value of the mean...
Bonus (5 points) Suppose that you are testing the following hypotheses: Ho: 4 = 10 and...
Bonus (5 points) Suppose that you are testing the following hypotheses: Ho: 4 = 10 and H :> 10. If the null hypothesis is rejected at the 1% level of significance, what statement can you make about the confidence interval on the mean? a) The lower bound of a 95% one-sided confidence interval on the mean exceeds 10. b) 9 <u< 13 c) No statement can be made. d) The lower bound of a 95% one-sided confidence interval on the...
1. Suppose that we are testing Hor = po versus H : > Ho with a sample size of n = 15. Calculate bounds on the P-value for the following observed values of the test statistic: (a) to = 2.35 (b) to = 3.55 (c) to = 1.55
2.11. Suppose that we are testing Ho: μ-μ0 versus H: >o with a sample size of n 15. Calculate bounds on the P-value for the following observed values of the test statistic: (a) to 2.35 (b)o 3.55 (c) 2.00 (d) to 1.55
Please solve 2.7, 2.8 and 2.9 problems.
2.7. Suppose that we are testing Ho : μ1 Ha versus Ho: > μ2 where the two sample sizes are ni n, 10. Both sample variances are unknown but assumed equal. Find bounds on the P-value for the following observed values of the test statistic. (a) to= 2.31 (b) toー3.60 (c) to-1.95 (d) 0-219 2.8. Consider the following sample data: 9.37, 13.04, 11.69, 8.21, 11.18, 10.41, 13.15, 11.51, 13.21, and 7.75. Is it...
Q4). Suppose that you are drawing a sample of random observations yyy2y, from a population that is normally distributed with a mean- u and variance 2. Derive the two-sided likelihood ratio test for testing Ho : μ Ho versus H! : μ where μ. μο. 123. (5 points)
Q4). Suppose that you are drawing a sample of random observations yyy2y, from a population that is normally distributed with a mean- u and variance 2. Derive the two-sided likelihood ratio test...
Question 21 In testing Ho: p1" p,-0 versus Ha: p1" p. 0, the computed value of the test statistic is z = 2 25 The P value for this two-tailed test is then Not yet answered Points out of 6.00 Flag question Question 22 Not yet answered Points out of 4.00 The two-sample t test is applicable in situations in which population distributions are both normal when population variances have unknown values, and at least one of the two sample...
Exercises 10.3. Let Xi . . . , x N μ, σ2), whereơ2 s known to be equal to 100. In testing Ho : 25vs. H :H>25,h What sample size n would be necessary if one wishes to reject Ho with probability at least 95 if μ 26? iid se that a coin is to be tossed n times, and you wish to test the hypothesis Ho:p-12 VS. Hi P> I/2 at a- .05. What sample size n would be...
Suppose X1, .., Xn is a random sample from a N(0, a2) population, where variance o are known. Consider testing Ho : 0 = O0 vs. Hi 0 700 Q1(4pt): Using Likelihood Ratio Test (LRT) to obtain a level a test that rejects Ho if Уп(X — во) VП(х — во) <21-a/2 21-a/2 or о Q2(1pt): Is the two-sided test derived in 1) an uniformly most powerful test? If not, briefly state your reasons Q3 (1pt): Note that the test...
A sample from a Normal distribution with an unknown mean u and known variance o = 45 was taken with n=9 samples giving sample mean of y = 3.6. (a) Construct a Hypothesis test with significance level a = 0.05 to test whether the mean is equal to 0 or it is greater than 0. What can you conclude based on the outcome of the sample? (b) Calculate the power of this test if the true value of the mean...
Bonus (5 points) Suppose that you are testing the following hypotheses: Ho: 4 = 10 and H :> 10. If the null hypothesis is rejected at the 1% level of significance, what statement can you make about the confidence interval on the mean? a) The lower bound of a 95% one-sided confidence interval on the mean exceeds 10. b) 9 <u< 13 c) No statement can be made. d) The lower bound of a 95% one-sided confidence interval on the...
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