2.) For a particular type of hypothesis test with a sample size of 25, ? = 0.01 and ? = 0.73. Find each of the following:
A.) The probability of a Type I error.
B.) The probability of a Type II error.
C.) The power of this test.
D.) What value of alpha would result in higher power for this test?
E.) What value of n would result in higher power for this test?
A.) The probability of a Type I error.
? = 0.01
B.) The probability of a Type II error.
? = 0.73
C.) The power of this test.
1 - ? = 1 - 0.73 = 0.27
Power = 0.27
D.) What value of alpha would result in higher power for this test?
? > 0.01
E.) What value of n would result in higher power for this test?
n > 25
2.) For a particular type of hypothesis test with a sample size of 25, ? =...
Which of the following statements is FALSE? a.) The power of a hypothesis test is the probability of not making a Type II error. b.) Alpha (α) is equal to the probability of making a Type I error. c.) The probability of rejecting the null hypothesis when the null hypothesis is true is called a Type I Error. d.) A smaller sample size would increase the effectiveness of a hypothesis test.
When conducting a hypothesis test for a given sample size, if the probability of a Type I error decrease, the the A. probability of incorrectly not rejecting the null hypothesis decreases. B. probability of incorrectly not rejecting the null hypothesis increases. C. probability of incorrectly rejecting the null hypothesis increases. D. probability of type II error decreases.
You take a random sample of size 30 and conduct a hypothesis test at the 5 % level of significance . If instead , you take a random sample of size 50 and conduct the same hypothesis test at the same 5 % level of significance , what can you say about the probability of a type I and type II error (all else being equal ) ? A. P (Type I errror ) decreases and P (Type II error...
In each of the following situations, find the necessary sample size. a. In the Consolidated Power hypothesis test of H0: μ ≤ 60 versus Ha: μ > 60, find the sample size needed to make the probability of a Type I error equal to .025 and the probability of a Type II error corresponding to the alternative value μa = 60.5 equal to .025. Here, assume σ equals 2. n = ______
Which of the following will increase the power of a significance test? (A) Increase the Type II Error probability (B) Increase the significance level alpha (C) Select a value for the alternative hypothesis closer to the value of the null hypothesis (D) Decrease the sample size. (E) Reject the null hypothesis only if the P-value is smaller than the level of significance.
Consider the following hypothesis test. H0: ≥ 10 H1: <10 The sample size is 120 and the standard deviation of the population is 5. Use a = 0.05. a. If the real value of the population mean is 9, what is the probability that the mean of the sample will lead us not to reject H0? b. What type of error would be committed if the real value of the population mean was 9 and we conclude...
Which of the following statements is FALSE? A.) A larger sample size would increase the effectiveness of a hypothesis test. B.) Alpha (α) is equal to the probability of making a Type I error. C.) Expanding the sample size can increase the power of a hypothesis test. D.) Reducing the significance level (α) can increase a test's effectiveness.
Test the hypothesis at α = 0.01 Describe what type I errors are
in this context. Compute the p-value for this test.
A 2 sided Confidence Interval for the mean is, in analogy to the 2-sided hypothesis test, a range of values under which you would fail to reject the null hypothesis By rewriting this statement about the rejection region, under the assumption the null hypothesis is true: into a statement about the interval for μ you construct the 2-sided...
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...
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,...