Can someone explain step by step
158-
since we know that probability of type 2 error = 1-power of test
= 1-0.8
=0.2
Can someone explain step by step 157. The power for a one-sided test of the null...
Your research supervisor wants you to test the null hypothesis H0: μ = 25 against the one-sided alternative hypothesis Ha: μ < 25. The population has a normal distribution with a variance of 16. You are told to use a sample size of 100 and a rejection region of . State the probability of a Type II error for this test of significance to four digits to the right of the decimal point under the alternative hypothesis that μ = 24.
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?
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 = ______
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...
You set up a two-sided hypothesis test for a population mean μ with a null hypothesis of H0:μ=100. You chose a significance level of α=0.05. The p-value calculated from the data is 0.12, and hence you failed to reject the null hypothesis. Suppose that after your analysis was completed and published, an expert informed you that the true value of μ is 104. How would you describe the result of your analysis? A) A Type 1 error was made because...
We are looking to calculate the power of a one-sided test from n independent observations from a N(μ, σ2) distribution with a null hypothesis of Ho : μ-μο and an alternative H1 : μ > μο. Supposing that we know σ2, we can form a test statistic o/Vn and reject the null hypothesis when T > 1.645. This test has level α = 0.05. We want a formula for the power of this test against the alternative that μ-A-This power...
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.
We are looking to calculate the power of a one-sided test from n independent observations Xi from a N(μ, σ2) distribution with a null hypothesis of Ho : μ-μ0 and an alternative H, : μ 〉 μ0. Supposing that we know σ2, we can form a test statistic T= and reject the null hypothesis when T 〉 1.645. This test has level α 0.05. We want a formula for the power of this test against the alternative that μ-74-This power...
Based on the power curve shown below, which one of the following statements is false? power 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.0 19 20 21 23 24 25 The probability of a type I error is 0.10 The probability of a type Il error when H 21 is equal to 0.26 The null hypothesis is H0: μ-20 The power of the test when μ-23 is 0.91.
For a given population with o = 10.5 lb. we want to test the null hypothesis j = 66.5 against the alternative hypothesis u # 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 å > 68.8. a) (3 points) What is the probability of a type l error? b) (4 points) What is the probability of a type II error and the power...