4. Take a random sample of size 16 from a normal distribution with mean 25 and...
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...
3. A random sample of size 16 is drawn from a normal distribution with o = 9.0 for the purpose of testing: Ho : = 30 versus HP:ll # 30. The experimenter chooses to define the critical region C to be the set of sample means lying in the interval (29.9, 30.1). (3.1) What level of significance does the test have? (3.2) Improve the test by changing the definition of C, assuming the same a is to be used.
2. Suppose that Xi, , Xn, n-: 25, form a random sample from a normal distribution with mean θ and variance 4. Consider the following hypotheses at α-0.05 Ho : θ-0 versus H1 : θ > 0. Derive the power function, π( 5), and evaluate it at θ--04,-02, 0,02, 0.4, 0.6, 0.8, 1. 2. Suppose that Xi, , Xn, n-: 25, form a random sample from a normal distribution with mean θ and variance 4. Consider the following hypotheses at...
A random sample of size 16 from a normal distribution with mu=3 produced a sample mean of 4.5. a. Is the x distrobution normal? explain b. compute the sample test statistic z under the null hypothesis Ho: mu =6.3 c. For H1: mu <6.3, estimate the P-value of the test statistic d. For a level of significance of 0.01 and the hypothesis of parts (b) and (c), do you reject or fail to reject the null hypothesis? explain.
Let X1, ..., Xn denote an independent random sample from a population with a Poisson distribution with mean . Derive the most powerful test for testing Ho : 1= 2 versus Ha: 1= 1/2.
Let X1, X2, . . . , Xn be a random sample of size n from a normal population with mean µX and variance σ ^2 . Let Y1, Y2, . . . , Ym be a random sample of size m from a normal population with mean µY and variance σ ^2 . Also, assume that these two random samples are independent. It is desired to test the following hypotheses H0 : σX = σY versus H1 : σX...
3. Suppose that X (X...,X) is a random sample from a uniform distribution of the interval [0,0], where the value of ? is unknown, and it is desired to test the hypotheses H: 0>2 [5] (a) Show that the uniform family f(x;0)-(1/0)1 om(r) : ? > 0 maxi-isnXi. has a monotone likelihood ratio in the statistic T(X)- X. whereX (n) [5] (b) Find a uniformly most powerful (UMP) test of level ? for testing Ho versus HI
Can anyone help me with this problem? Thank you! 7. Let X1,.. , Xn denote a random sample from (1-9)/0 x; Test Ho: θ Bo versus H1: θ θο. (a) For a sample of size n, find a uniformly most powerful (UMP) size-a test if such exists. (b) Take n-?, θ0-1, and α-.05, and sketch the power function of the UMP test. 7. Let X1,.. , Xn denote a random sample from (1-9)/0 x; Test Ho: θ Bo versus H1:...
the unknown Popular random sample of size 17 is obtained from a normal (15) 4.Malding a sample standard deviation of S. Teet the nuit that the unknown population variance is greater than or 169, versus the alternative hypothesis that the unknown lance is less than 169 using a 1% level of significance hypothesis that Set up the null and alternative hypotheses, clearly defining any unknown parameters. Note the value is always in the mull hypothesis m atatest statistie: (1) sensitive...
Exercise: Let Yİ,Y2, ,, be a random sample from a Gamma distribution with parameters and β. Assume α > 0 is known. a. Find the Maximum Likelihood Estimator for β. b. Show that the MLE is consistent for β. c. Find a sufficient statistic for β. d. Find a minimum variance unbiased estimator of β. e. Find a uniformly most powerful test for HO : β-2 vs. HA : β > 2. (Assume P(Type!Error)- 0.05, n 10 and a -...