The power of a test against a specific alternative is computed as ________.
Group of answer choices
A: 1- Type I error
B: Type II error
C: None of the above.
Answer:
B: Type II error
Solution:
We know that the power of the test against a specific alternative is computed as the 1 minus type II error by assuming that alternative hypothesis is true.
The power of a test against a specific alternative is computed as ________. Group of answer...
The "power of a test" is the probability of concluding HA when in fact HA is true. The power of a test will decrease if: Group of answer choices There is low variability amongst the population being studied. A larger sample is used. Data is collected or measured in a more consistent fashion. A lower significance level (alpha) is used. Part B The significance level (alpha) represents all the following EXCEPT: Group of answer choices Your willingness to make a...
Select the correct definition of the p-value of a test from the answer choices below: The probability that the null hypothesis is true The probability that, assuming the null hypothesis is true, we obtained a test statistic as or more extreme than what we calculated The probability that, assuming the alternative hypothesis is true, we obtained a test statistic as or more extreme than what we calculated The probability that the alternative hypothesis is false, given that the null hypothesis...
1. a) For a test at a fixed significance level, and with given null and alternative hypotheses, what will happen to the power as the sample size increases? b) For a test of a given null hypothesis against a given alternative hypothesis, and with a given sample size, describe what would happen to the power of the test if the significance level was changed from 5% to 1%. c) A test of a given null hypothesis against a given alternative...
1. It is desired to test the null hypothesis u = 40 against the alternative hypothesis u < 40 on the basis of a random sample from a population with standard deviation 4. If the probability of a Type I error is to be 0.04 and the probability of Type II error is to be 0.09 for u = 38, find the required size of the sample.
18 marks] Suppose X~N(0,0). We wish to use a single value X hypothesis to test the null against the alternative hypothesis Denote by C aa) the critical region of a test at the significance level of -0.05 (a) 2 marks] What is the sample space S, the parameter space 9 space Θο of the test? and the null parameter (b) 12 marks) Computea (c) 12 marks Compute the power of the test (i.e., at 2) (d) [2 marks] Compute the...
For a given population with σ=10.5 lb. we want to test the null hypothesis μ=66.5 against the alternative hypothesis μ ≠66.5 on the basis of a random sample of size n=64. If the null hypothesis is rejected when x¯<64.6 lb. or x¯>68.8. a) (3 points) What is the probability of a type I error? b) (4 points) What is the probability of a type II error and the power of the test when in reality μ=67.0?
Suppose you want to test H0 : µ = 4 against Ha : µ > 4. In addition, suppose that σ = 5, n = 36, and you will reject H0 if x > 5 and accept H0 otherwise. (a) (6 pts) Find the power of this test against the alternative µ = 5.6. (b) (2 pts) Find the probability of a Type II error in this situation (just use your answer from part (a) to help you do this).
QUESTION 35 What is the relationship between the power of a test and the types of errors you can make? The power of a test is equal to 1 minus the probability of a Type II error. The power of a test is equal to the sum of the probabilities of a Type I and Type II error. The power of a test is equal to 1 minus the probability of a Type I error. There is no relationship between...
In a two-tail test for the population mean, if we decided in favor of the alternative hypothesis when the null hypothesis is false, A. a Type II error is made B. a one-tail test should be used instead of a two-tail test C. a correct decision is made D. a Type I error is made In a one-tail test for the population mean, if we decide in favor of the null hypothesis when the alternative hypothesis is true, A. a...
=1 against H :1 2. consider the 2. A sample of size 1 is taken from a Poisson(A) distribution. To test Ho : test 1 X > 3 (x) = { X 53 (a) What is the probability of making a Type I error? (b) What is the probability of making a Type II error? (c) What is the power of the test if 27 How does this connect to your answers above? Explain.