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1. Assume that the daily profits X of a certain company has a normal distribution with unknown me...
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...
Suppose is a random sample from exponential distribution having unknown mean . We wish to test vs. . Consider the following tests: Test 1: Reject if and only if ; Test 2: Reject if and only if...
Suppose is a random sample from exponential distribution having unknown mean . We wish to test vs. . Consider the following tests: Test 1: Reject if and only if ; Test 2: Reject if and only if Find the power of each test at . We were unable to transcribe this imageWe were unable to transcribe this imageHo : θ = 4 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this...
1-2.Assume that the height of male students at Anytown State University is normally distributed with (unknown)...
1-2.Assume that the height of male students at Anytown State University is normally distributed with (unknown) mean μ and standard deviation σ-2.4 inches. A random sample of n -9 male students is obtained. 2. a) b) We wish to test H0:μ=69 Hi : μ#69. vs. The average height of the students in the sample was 70.2 inches. Find the p-value. Find the Rejection Region for the test at a -0.05. Tha is, for which values of the sample mean X...
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,...
2. The daily profit X from a drink vending machine placed in the entrance area of a school buildi...
2. The daily profit X from a drink vending machine placed in the entrance area of a school building of a university follows the normal distribution N(μ, σ2) with unknown μ and σ2. Naturally, the mean (the average daily profit) varies from building to building. Based on past experience, it is determined that μ follows a normal distribution with mean μ°-$30 and standard deviation Do $1.75. If one of these drink machines in a certain building shows an average daily...
9. (1 mark) The distribution of systolic blood pressure for a population of adult males is...
9. (1 mark) The distribution of systolic blood pressure for a population of adult males is Normal with σ-15. A SRS of 49 adult males is taken from this population and systolic blood pressure is measured for each man. A test of the hypothesis H0: μ 120 versus Ha: μメ120 rejects H0 at the 5% level if z--1.960 or z 〉 1.960 (in other words when |z > 1.960) where T120 15/V49 round your answer to at least 3 decimal...
Problem 13.2 Assume that Xi, X2,. Xa form a random sample from a normal distribution for which th...
Problem 13.2 Assume that Xi, X2,. Xa form a random sample from a normal distribution for which the mean μ is unknown and the variance is 1 . Suppose the following are to be tested: H:H>0 hypotheses at the level of significance α,-0.025 and Let δ. denote the UMP test of these let π(u 18) denote the power function of the test procedure δ a) The yMP test rejects Ho when X 2 c. Determine the appropriate value for c...
Now consider the above problem in a different way: Assume that X is following a normal...
Now consider the above problem in a different way: Assume that X is following a normal distribution with mean u and known variance σ2 4. We want to test H0 : μ 1 vs. H1 : μ-2 based on a sample of size n. The decision rule is to reject Ho if R Find n and c such that α 0.05 and β = 0.05. c.
Assume that x has a normal distribution with the specified mean and standard deviation. Find the...
Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) μ = 8; σ = 2 P(7 ≤ x ≤ 11) = Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) μ = 6.0; σ = 1.4 P(7 ≤ x ≤ 9) = Assume that x has a normal...
Software can generate samples from (almost) exactly Normal distributions. Here is a random sample of size...
Software can generate samples from (almost) exactly Normal distributions. Here is a random sample of size 5 from the Normal distribution with mean 8 and standard deviation 2: 4.47 5.51 8.1 11.63 7.91 Although we know the true value of μ suppose we pretend that we do not and we test the hypotheses Ho : μ-5.6 a:μ 5.6 at the α 0.05 significance level. What is the power of the test against the alternative μ 8 (the actual population mean)?...
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...
1-2.Assume that the height of male students at Anytown State University is normally distributed with (unknown) mean μ and standard deviation σ-2.4 inches. A random sample of n -9 male students is obtained. 2. a) b) We wish to test H0:μ=69 Hi : μ#69. vs. The average height of the students in the sample was 70.2 inches. Find the p-value. Find the Rejection Region for the test at a -0.05. Tha is, for which values of the sample mean X...
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,...
2. The daily profit X from a drink vending machine placed in the entrance area of a school building of a university follows the normal distribution N(μ, σ2) with unknown μ and σ2. Naturally, the mean (the average daily profit) varies from building to building. Based on past experience, it is determined that μ follows a normal distribution with mean μ°-$30 and standard deviation Do $1.75. If one of these drink machines in a certain building shows an average daily...
9. (1 mark) The distribution of systolic blood pressure for a population of adult males is Normal with σ-15. A SRS of 49 adult males is taken from this population and systolic blood pressure is measured for each man. A test of the hypothesis H0: μ 120 versus Ha: μメ120 rejects H0 at the 5% level if z--1.960 or z 〉 1.960 (in other words when |z > 1.960) where T120 15/V49 round your answer to at least 3 decimal...
Problem 13.2 Assume that Xi, X2,. Xa form a random sample from a normal distribution for which the mean μ is unknown and the variance is 1 . Suppose the following are to be tested: H:H>0 hypotheses at the level of significance α,-0.025 and Let δ. denote the UMP test of these let π(u 18) denote the power function of the test procedure δ a) The yMP test rejects Ho when X 2 c. Determine the appropriate value for c...
Now consider the above problem in a different way: Assume that X is following a normal distribution with mean u and known variance σ2 4. We want to test H0 : μ 1 vs. H1 : μ-2 based on a sample of size n. The decision rule is to reject Ho if R Find n and c such that α 0.05 and β = 0.05. c.
Software can generate samples from (almost) exactly Normal distributions. Here is a random sample of size 5 from the Normal distribution with mean 8 and standard deviation 2: 4.47 5.51 8.1 11.63 7.91 Although we know the true value of μ suppose we pretend that we do not and we test the hypotheses Ho : μ-5.6 a:μ 5.6 at the α 0.05 significance level. What is the power of the test against the alternative μ 8 (the actual population mean)?...
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