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(18.52) You have an SRS of size n = 11 from a Normal distribution with s...
Use R to find to find the answers to the problems 2. (25 points) Suppose that we have a sample of size n 64, we know the population standard deviation is σ 48, and we are considering a normal...
Use R to find to find the answers to the problems
2. (25 points) Suppose that we have a sample of size n 64, we know the population standard deviation is σ 48, and we are considering a normally distributed population, we want to test the hypotheses: Ho : μ-200 Hi 200 We are going to use a z-test because σ is known. We will use a significance level of:-0.05. (a) What is the critica z value? In other words,...
5. (worth 16 points) Consider a test of H : μ-65 versus Ha μ > 65. The test uses σ-10, α-01 size of n 64. and a samp...
5. (worth 16 points) Consider a test of H : μ-65 versus Ha μ > 65. The test uses σ-10, α-01 size of n 64. and a sample a. Describe the sampling distribution of Fassuming Ho is true. Mean (t)- Standard deviation (oz)- Shape: Sketch the sampling distribution of x assuming Ho is true is used as the test stat istic. Locate the rejection region on your graph from b. Specify the rejection region when x part a. C. Describe...
Please show work. Thanks in advance. Question 5 (20 pts) You must decide which of two...
Please show work. Thanks in advance.
Question 5 (20 pts) You must decide which of two discrete distri- butions a random variable X has. We will call the distributions po and p. Here are the probabilities they assign to the values r of X. 2 Po P 0 1 2 0.1 0.1 0.2 0.1 0.3 0.2 3 4 5 0.3 0.1 0.1 0.1 0.1 0.1 6 0.1 0.1 You have a single observation on X and wish to test Ho:...
4) Your company manufactures 200 mg ibuprofen tablets. You randomly sample 25 tablets and measure...
please solve both questions 4&5 and solve all parts.
4) Your company manufactures 200 mg ibuprofen tablets. You randomly sample 25 tablets and measure their mass, then calculate the average mass X from this sample. You know that the standard deviation of tablet mass from your manufacturing process is ơ- 0 mg a. Specify a null and alternative process to determine whether or the mass of ibuprofen tablets from your process is 200 mg b. You reject the null hypothesis...
A mixture of pulverized fuel ash and Portland cement to be used for grouting should have...
A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more than 1300 KN/m2. The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed with σ-70. Let μ denote the true average compressive strength. a) What are the a null and altenative hypotheses? Ho: 1300 на: #1300 Ho:> 1300 hja: μ-1300...
2. Suppose that we have n independent observations x1, ,Tn from a normal distribution with mean...
2. Suppose that we have n independent observations x1, ,Tn from a normal distribution with mean μ and variance σ2, and we want to test (a) Find the maximum likelihood estimator of μ when the null hypothesis is true. (b) Calculate the Likelihood Ratio Test Statistic 7-2 log max L(μ, σ*) )-2 log ( max L(u, i) μισ (c) Explain as clearly as you can what happens to T, when our estimate of σ2 is less than 1. (d) Show...
2. Suppose that we have 9 independent observations from a normal distribution with standard deviation 10....
2. Suppose that we have 9 independent observations from a normal distribution with standard deviation 10. We wish to test Ho : μ-150 vs. H A : μ 150 The best test with level a- 0.05 uses the test statistic T1 =1元-1501 and has a critical value of c 6.53. The test rejects the null hypothesis when T> c (a) Calculate the power of this test against the alternative μ-151. (b) Calculate the power of this test against the alternative...
1) You have a process to detect surface flaws on an orthopedic device. Your process is...
1) You have a process to detect surface flaws on an orthopedic device. Your process is correct 70% of the time with current employees, and you are hoping that newer employees will perform better when executing your process due to improved training methods. a. Specify a null and alternative process to determine whether your newer employees perform as well as your experienced employees. b. You decide to reject the null hypothesis Ho: p= 0.7 if newer employees correctly identify flaws...
Suppose that X ~ POI(μ), where μ > 0. You will need to use the following fact: when μ is not too close to 0, VR ape x N(VF,1/4). (a) Suppose that we wish to test Ho : μ-710 against Ha : μ μί a...
Suppose that X ~ POI(μ), where μ > 0. You will need to use the following fact: when μ is not too close to 0, VR ape x N(VF,1/4). (a) Suppose that we wish to test Ho : μ-710 against Ha : μ μί are given and 10 < μι. m, where 140 and Using 2 (Vx-VHo) as the test statistic, find a critical region (rejection region) with level approximately a (b) Now suppose that we wish to test Ho...
2. Let X1,.n be a random sample from the density 0 otherwise Suppose n = 2m+...
2. Let X1,.n be a random sample from the density 0 otherwise Suppose n = 2m+ 1 for some integer m. Let Y be the sample median and Z = max(Xi) be the sample maximum (a) Apply the usual formula for the density of an order statistic to show the density of Y is (b) Note that a beta random variable X has density f(x) = TaT(可 with mean μ = α/(a + β) and variance σ2 = αβ/((a +s+...
Use R to find to find the answers to the problems
2. (25 points) Suppose that we have a sample of size n 64, we know the population standard deviation is σ 48, and we are considering a normally distributed population, we want to test the hypotheses: Ho : μ-200 Hi 200 We are going to use a z-test because σ is known. We will use a significance level of:-0.05. (a) What is the critica z value? In other words,...
5. (worth 16 points) Consider a test of H : μ-65 versus Ha μ > 65. The test uses σ-10, α-01 size of n 64. and a sample a. Describe the sampling distribution of Fassuming Ho is true. Mean (t)- Standard deviation (oz)- Shape: Sketch the sampling distribution of x assuming Ho is true is used as the test stat istic. Locate the rejection region on your graph from b. Specify the rejection region when x part a. C. Describe...
Please show work. Thanks in advance.
Question 5 (20 pts) You must decide which of two discrete distri- butions a random variable X has. We will call the distributions po and p. Here are the probabilities they assign to the values r of X. 2 Po P 0 1 2 0.1 0.1 0.2 0.1 0.3 0.2 3 4 5 0.3 0.1 0.1 0.1 0.1 0.1 6 0.1 0.1 You have a single observation on X and wish to test Ho:...
please solve both questions 4&5 and solve all parts.
4) Your company manufactures 200 mg ibuprofen tablets. You randomly sample 25 tablets and measure their mass, then calculate the average mass X from this sample. You know that the standard deviation of tablet mass from your manufacturing process is ơ- 0 mg a. Specify a null and alternative process to determine whether or the mass of ibuprofen tablets from your process is 200 mg b. You reject the null hypothesis...
A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more than 1300 KN/m2. The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed with σ-70. Let μ denote the true average compressive strength. a) What are the a null and altenative hypotheses? Ho: 1300 на: #1300 Ho:> 1300 hja: μ-1300...
2. Suppose that we have n independent observations x1, ,Tn from a normal distribution with mean μ and variance σ2, and we want to test (a) Find the maximum likelihood estimator of μ when the null hypothesis is true. (b) Calculate the Likelihood Ratio Test Statistic 7-2 log max L(μ, σ*) )-2 log ( max L(u, i) μισ (c) Explain as clearly as you can what happens to T, when our estimate of σ2 is less than 1. (d) Show...
2. Suppose that we have 9 independent observations from a normal distribution with standard deviation 10. We wish to test Ho : μ-150 vs. H A : μ 150 The best test with level a- 0.05 uses the test statistic T1 =1元-1501 and has a critical value of c 6.53. The test rejects the null hypothesis when T> c (a) Calculate the power of this test against the alternative μ-151. (b) Calculate the power of this test against the alternative...
1) You have a process to detect surface flaws on an orthopedic device. Your process is correct 70% of the time with current employees, and you are hoping that newer employees will perform better when executing your process due to improved training methods. a. Specify a null and alternative process to determine whether your newer employees perform as well as your experienced employees. b. You decide to reject the null hypothesis Ho: p= 0.7 if newer employees correctly identify flaws...
Suppose that X ~ POI(μ), where μ > 0. You will need to use the following fact: when μ is not too close to 0, VR ape x N(VF,1/4). (a) Suppose that we wish to test Ho : μ-710 against Ha : μ μί are given and 10 < μι. m, where 140 and Using 2 (Vx-VHo) as the test statistic, find a critical region (rejection region) with level approximately a (b) Now suppose that we wish to test Ho...
2. Let X1,.n be a random sample from the density 0 otherwise Suppose n = 2m+ 1 for some integer m. Let Y be the sample median and Z = max(Xi) be the sample maximum (a) Apply the usual formula for the density of an order statistic to show the density of Y is (b) Note that a beta random variable X has density f(x) = TaT(可 with mean μ = α/(a + β) and variance σ2 = αβ/((a +s+...
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