![(10 pts) One generates a number z from a uniform distribution on the interval [0.0]. 2 by rejecting Ho if r 0.1 or z > 19. : θ One decides to test Ho : θ 2 against 10 (a) Compute the probability of to have type I error. (b) Find the power for this test if the true value of θ is 2.5.](http://img.homeworklib.com/questions/b1465540-6ff3-11ea-a527-2b2bf820eefb.png?x-oss-process=image/resize,w_560)
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(10 pts) One generates a number z from a uniform distribution on the interval [0.0]. 2...
(10 pts) One generates a number r from a uniform distribution on the interval [0,6 One...
(10 pts) One generates a number r from a uniform distribution on the interval [0,6 One decides to test Ho: 0 2 against Ho:82 by rejecting Ho if S0.1 orr 2 1.9. (a) Compute the probability of to have type I error (b) Find the power for this test if the true value of θ is 2.5.
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 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,...
A random variable, X, has uniform distribution on the interval [0,θ] where θ is unknown. A...
A random variable, X, has uniform distribution on the interval [0,θ] where θ is unknown. A hypothesis test is as follows: H0: θ = 2 H1: θ ≠ 2 It has been decided to reject H0 if the observed value of x is x ≤ 0.1 or x ≥ 1.9. Part a: Find the probability of committing a Type I error. Part b: Suppose the true value of θ is 3. Find the probability of committing a Type II error....
D Chapter 15 Problem Set Suppose you are planning a study that will est the following one-tailed ...
D Chapter 15 Problem Set Suppose you are planning a study that will est the following one-tailed hypotheses: To evaluate the power of your study, you consider a specific alternative hypothesis, μ-Ha, where μ.> μ。. The following sketch shows two overlapping sampling distributions of X-one when Ho is true (and H1 is false), the other when Hy is true (and Ho is false). The distribution on the left has a mean of yo and represents the sampling distribution of X...
4. An exponential random variable X has p.d.f (x,07/», x>0, c.df. F(x:0) 1-exp(-x/8) for x >...
4. An exponential random variable X has p.d.f (x,07/», x>0, c.df. F(x:0) 1-exp(-x/8) for x > 0, and mean θ. A single observation of an exponential random variable X is used to test H0 : θ-2 against H1 : θ-5. The null hypothesis is accepted if and only if the observed value of the random variable is less than 3. (a) What is the probability of committing a Type I error? (b) What is the probability of committing a Type...
1. Let Y1, . . . ,Y,, be a random sample from a population with density...
1. Let Y1, . . . ,Y,, be a random sample from a population with density function 0, otherwise (a) Find the method of moments estimator of θ (b) Show that Yan.-max(Yi, . . . ,%) is sufficient for 02] (Hint: Recall the indicator function given by I(A)1 if A is true and 0 otherwise.) (c) Determine the density function of Yn) and hence find a function of Ym) that is an unbiased estimator of θ (d) Find c so...
Please answer this question using R 20. Let X1, X2, ..., X12 be a random sample...
Please answer this question using R
20. Let X1, X2, ..., X12 be a random sample from a Bernoulli distribution with unknown success probability p. We will test Ho: p = 0.3 versus Ha: p < 0.3, rejecting the null if the number of successes, Y = Dizi Xi, is 0 or 1. (a) Find the probability of a Type I error. (b) If the alternative is true, find an expression for the power, 1 – B, as a function...
Additional GO Tutorial Problem 9.001 A manufacturer is interested in the output voltage of a power...
Additional GO Tutorial Problem 9.001 A manufacturer is interested in the output voltage of a power supply used in a PC. Output voltage is assumed to be normally distributed, with standard deviation 0.25 V, and the manufacturer wished to test Ho: 9 V against H: 9 V, using n = 10 units. Statistical Tables and Charts Good. The probability of rejecting Ho when it is true is approximately 4%. (a) The critical region is x < 8.84 or X >...
I would like the whole Question done on r studio with the R Code. 1. In...
I would like the whole Question done on r studio with
the R Code.
1. In this question we will evaluate type I and type II error probabilities for one-sided tests. We will consider normally distributed data, with unit variance and independent obervations. We will use Ho : μ-0 for the null and H1 : μ-1 for the alternative, unless otherwise stated. (a) Suppose we have n-6 observationsx. What is the sampling distribution of the (10 marks) sample mean (that...
(10 pts) One generates a number r from a uniform distribution on the interval [0,6 One decides to test Ho: 0 2 against Ho:82 by rejecting Ho if S0.1 orr 2 1.9. (a) Compute the probability of to have type I error (b) Find the power for this test if the true value of θ is 2.5.
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,...
D Chapter 15 Problem Set Suppose you are planning a study that will est the following one-tailed hypotheses: To evaluate the power of your study, you consider a specific alternative hypothesis, μ-Ha, where μ.> μ。. The following sketch shows two overlapping sampling distributions of X-one when Ho is true (and H1 is false), the other when Hy is true (and Ho is false). The distribution on the left has a mean of yo and represents the sampling distribution of X...
4. An exponential random variable X has p.d.f (x,07/», x>0, c.df. F(x:0) 1-exp(-x/8) for x > 0, and mean θ. A single observation of an exponential random variable X is used to test H0 : θ-2 against H1 : θ-5. The null hypothesis is accepted if and only if the observed value of the random variable is less than 3. (a) What is the probability of committing a Type I error? (b) What is the probability of committing a Type...
1. Let Y1, . . . ,Y,, be a random sample from a population with density function 0, otherwise (a) Find the method of moments estimator of θ (b) Show that Yan.-max(Yi, . . . ,%) is sufficient for 02] (Hint: Recall the indicator function given by I(A)1 if A is true and 0 otherwise.) (c) Determine the density function of Yn) and hence find a function of Ym) that is an unbiased estimator of θ (d) Find c so...
Please answer this question using R
20. Let X1, X2, ..., X12 be a random sample from a Bernoulli distribution with unknown success probability p. We will test Ho: p = 0.3 versus Ha: p < 0.3, rejecting the null if the number of successes, Y = Dizi Xi, is 0 or 1. (a) Find the probability of a Type I error. (b) If the alternative is true, find an expression for the power, 1 – B, as a function...
Additional GO Tutorial Problem 9.001 A manufacturer is interested in the output voltage of a power supply used in a PC. Output voltage is assumed to be normally distributed, with standard deviation 0.25 V, and the manufacturer wished to test Ho: 9 V against H: 9 V, using n = 10 units. Statistical Tables and Charts Good. The probability of rejecting Ho when it is true is approximately 4%. (a) The critical region is x < 8.84 or X >...
I would like the whole Question done on r studio with
the R Code.
1. In this question we will evaluate type I and type II error probabilities for one-sided tests. We will consider normally distributed data, with unit variance and independent obervations. We will use Ho : μ-0 for the null and H1 : μ-1 for the alternative, unless otherwise stated. (a) Suppose we have n-6 observationsx. What is the sampling distribution of the (10 marks) sample mean (that...
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