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Problem 1 Let X is amount of coffee in a "100g coffee can"), EX μ. With...
Solve please Problem 1 Let X is amount of coffee in a "100g coffee can"), EX...
Solve please
Problem 1 Let X is amount of coffee in a "100g coffee can"), EX μ. With a sample of size 25 you test null of μ-100 against μ > 100 at 5% significance level. Let X ~ N(μ, σ2) and variance is known: σ- 1 . (a) Find the decision rule for that test. (b) Suppose, actually μ= <100. What will be the probability to reject null of μ= 100 in favor of the alternative μ > 100...
Solve only b Problem 1 Let X is amount of coffee in a "100g coffee can"),...
Solve only b
Problem 1 Let X is amount of coffee in a "100g coffee can"), EX μ. With a sample of size 25 you test null of μ-100 against μ > 100 at 5% significance level. Let X ~ N(μ, σ2) and variance is known: σ- 1 . (a) Find the decision rule for that test. (b) Suppose, actually μ= <100. What will be the probability to reject null of μ= 100 in favor of the alternative μ >...
Problem 1 Let X is amount of coffee in a "l00g coffee can"), EX μ. With...
Problem 1 Let X is amount of coffee in a "l00g coffee can"), EX μ. With a sample of size 25 you test null of μ-100 against μ > 100 at 5% significance level. Let X ~ N(μ, σ2) and variance is known: σ 1 . (a) Find the decision rule for that test. (b) Suppose, actually μ= <100. What will be the probability to reject null of μ= 100 in favor of the alternative μ > 100 in that...
10 Problem 1 Let X is amount of coffeein a "100g coffeecan), EXu. With a sample...
10 Problem 1 Let X is amount of coffeein a "100g coffeecan), EXu. With a sample of size 25 you test null of coffee can"), . Let X ~N(μ, σ2) and variance is known: σ- s amount of coffee in a against μ > 100 at 5% significance level (a) Find the decision rule for that test. (b) Suppose, actually100. What will be the probability to reject null of alternative μ > 100 in that case? Plot that probability as...
Problem 1 A student decided to perform at 5% sigfnificance level usual t-test for H:4=3 against...
Problem 1 A student decided to perform at 5% sigfnificance level usual t-test for H:4=3 against H:4 3, for a sample of size n=10. But she did a mistake: used wrong degrees of freedom df - 10 instead of correct df - 11-1-9, so she used wrong critical value. What is the probability of type I error that she would have performing the test? Problem 2 Let X is amount of coffee in a "100g coffee can", EX = 4....
2. A randon sample XI, X. is drawn frotn Normal(μ, σ2), where-oo < μ < oo and 0 < σ2 < x. To test the null hypothesis Ho : σ2-1 against the alternative H1: σ2 > 1, we have designed the...
2. A randon sample XI, X. is drawn frotn Normal(μ, σ2), where-oo < μ < oo and 0 < σ2 < x. To test the null hypothesis Ho : σ2-1 against the alternative H1: σ2 > 1, we have designed the following test Reject Ho if S>k where S2 = "LE:-1(x,-X)2, k ís a constant. Noticed that (n-1) distribution with degree of freedom 1 has a (a) Determine k so that the test will have size a. (b) Use k...
A machine in the student lounge dispenses coffee. The average cup of coffee is supposed to contai...
A machine in the student lounge dispenses coffee. The average cup of coffee is supposed to contain 7.0 ounces. A random sample of eight cups of coffee from this machine show the average content to be 7.4 ounces with a standard deviation of 0.70 ounce. Do you think that the machine has slipped out of adjustment and that the average amount of coffee per cup is different from 7 ounces? Use a 5% level of significance. What are we testing...
---------------------------------------------------------------------------------------------------------------------------------------------------------- Reference: 11.2.3 Suppose that X. , X are...
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Reference:
11.2.3 Suppose that X. , X are iid MI, σ2) where σ (E 9t*) is the unknown parameter but μ(€ 9) is assumed known. With preassigned α ε (0. 1), derive a level α LR test for a null hypothesis Ho : σ.-a> 0) against an alternative hypothesis H, : σ2 σ1 in the implementable form. {Note: Recall from the Exercise 8.5.5 that no UMP level a test exists for testing Ho versus 8.5.5 Let X, X, be...
8. Suppose that Xi,..., Xn is a sample from a normal population having unknown pa- rameters μ and...
8. Suppose that Xi,..., Xn is a sample from a normal population having unknown pa- rameters μ and σ2 a) Devise a significance level α test of the null hypothesis 0 versus the alternative hypothesis for a given positive value σ1. b) Explain how the test would be modified if the population mean μ were known in advance
8. Suppose that Xi,..., Xn is a sample from a normal population having unknown pa- rameters μ and σ2 a) Devise a...
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,...
Solve please
Problem 1 Let X is amount of coffee in a "100g coffee can"), EX μ. With a sample of size 25 you test null of μ-100 against μ > 100 at 5% significance level. Let X ~ N(μ, σ2) and variance is known: σ- 1 . (a) Find the decision rule for that test. (b) Suppose, actually μ= <100. What will be the probability to reject null of μ= 100 in favor of the alternative μ > 100...
Solve only b
Problem 1 Let X is amount of coffee in a "100g coffee can"), EX μ. With a sample of size 25 you test null of μ-100 against μ > 100 at 5% significance level. Let X ~ N(μ, σ2) and variance is known: σ- 1 . (a) Find the decision rule for that test. (b) Suppose, actually μ= <100. What will be the probability to reject null of μ= 100 in favor of the alternative μ >...
Problem 1 Let X is amount of coffee in a "l00g coffee can"), EX μ. With a sample of size 25 you test null of μ-100 against μ > 100 at 5% significance level. Let X ~ N(μ, σ2) and variance is known: σ 1 . (a) Find the decision rule for that test. (b) Suppose, actually μ= <100. What will be the probability to reject null of μ= 100 in favor of the alternative μ > 100 in that...
10 Problem 1 Let X is amount of coffeein a "100g coffeecan), EXu. With a sample of size 25 you test null of coffee can"), . Let X ~N(μ, σ2) and variance is known: σ- s amount of coffee in a against μ > 100 at 5% significance level (a) Find the decision rule for that test. (b) Suppose, actually100. What will be the probability to reject null of alternative μ > 100 in that case? Plot that probability as...
Problem 1 A student decided to perform at 5% sigfnificance level usual t-test for H:4=3 against H:4 3, for a sample of size n=10. But she did a mistake: used wrong degrees of freedom df - 10 instead of correct df - 11-1-9, so she used wrong critical value. What is the probability of type I error that she would have performing the test? Problem 2 Let X is amount of coffee in a "100g coffee can", EX = 4....
2. A randon sample XI, X. is drawn frotn Normal(μ, σ2), where-oo < μ < oo and 0 < σ2 < x. To test the null hypothesis Ho : σ2-1 against the alternative H1: σ2 > 1, we have designed the following test Reject Ho if S>k where S2 = "LE:-1(x,-X)2, k ís a constant. Noticed that (n-1) distribution with degree of freedom 1 has a (a) Determine k so that the test will have size a. (b) Use k...
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Reference:
11.2.3 Suppose that X. , X are iid MI, σ2) where σ (E 9t*) is the unknown parameter but μ(€ 9) is assumed known. With preassigned α ε (0. 1), derive a level α LR test for a null hypothesis Ho : σ.-a> 0) against an alternative hypothesis H, : σ2 σ1 in the implementable form. {Note: Recall from the Exercise 8.5.5 that no UMP level a test exists for testing Ho versus 8.5.5 Let X, X, be...
8. Suppose that Xi,..., Xn is a sample from a normal population having unknown pa- rameters μ and σ2 a) Devise a significance level α test of the null hypothesis 0 versus the alternative hypothesis for a given positive value σ1. b) Explain how the test would be modified if the population mean μ were known in advance
8. Suppose that Xi,..., Xn is a sample from a normal population having unknown pa- rameters μ and σ2 a) Devise a...
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,...
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