4)
P(tyoe I error) = α = 0.05
P(Type II error) = 1 - power = 1 - 0.82 = 0.18
5)
P(Type II error) = 1 - power = 1 - 0.1 = 0.90
The National Assessment of Educational Progress says that a score of 275 or higher on its...
Suppose that scores on the mathematics part of the National Assessment of Educational Progress (NAEP) test for eighth-grade students follows a normal distribution with sd equal to 110. You want to estimate the true mean score within +/- 10 points with 90% confidence. Suppose you find out that the most you can sample is only 225 subjects. Now estimate the confidence level you could attain with n=225.
You read that a statistical test at the α=0.01 level has probability 0.14 of making a Type II error when a specific alternative is true. What is the power of the test against this alternative? Suppose we tested the null hypothesis that the weight of a McDonald's quarter pounder is 0.25 pounds (H0 : µ = 0.25) against the alternative that the weight is below 0.25 pounds (Ha : µ < 0.25). After collecting a sample our observed z statistic...
You read that a statistical test at the α=0.01 level has probability 0.14 of making a Type II error when a specific alternative is true. What is the power of the test against this alternative? Suppose we tested the null hypothesis that the weight of a McDonald's quarter pounder is 0.25 pounds (H0 : µ = 0.25) against the alternative that the weight is below 0.25 pounds (Ha : µ < 0.25). After collecting a sample our observed z statistic...
1. Which of the following will increase the value of the power in a statistical test of hypotheses? (a) Increase the Type II error probability. (b) Increase the sample size. (c) Reject the null hypothesis only if the P-value is smaller than the level of significance. (d) All of the above 2. A significance test gives a P-value of 0.023. This means that the result is statistically significant at (a) both the 0.01 and the 0.05 levels. (b) neither the...
1. In testing hypotheses, the researcher initially assumes that the alternative hypothesis is true and uses the sample data to reject it. True False 2. The first step in testing a hypothesis is to establish a true null hypothesis and a false alternative hypothesis. True False 6. The power curve provides the probability of Correctly accepting the null hypothesis Incorrectly accepting the null hypothesis Correctly rejecting the alternative hypothesis Correctly rejecting the null hypothesis 7. Suppose that Ho: μ ≤...
Suppose the null hypothesis is Ho : µ = 500 against Ha : > µ = 500 , and the significance level for this testing is 0.05. The population in question is normally distributed with standard deviation 100. A random sample of size n=25 will be used. If the true alternative mean is 550, then the probability of committing the type II error is ____.
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...
4. An exponential random variable X has p.d.f (x,07/», x>0, c.df. F(x:0) 1-exp(-x/8) for x > 0, and mean θ. A single observation of an exponential random variable X is used to test H0 : θ-2 against H1 : θ-5. The null hypothesis is accepted if and only if the observed value of the random variable is less than 3. (a) What is the probability of committing a Type I error? (b) What is the probability of committing a Type...
It's a multi part question set - if you can't finish all of it, that's ok! I would just really appreciate any and all help as soon as possible, will give thumbs up, thank you so much in advance! Thank you!! Inventory management There are 13 questions in this set As you proceed through these questions, use necessary information from previous questions. Walzon recently made changes to its inventory management and delivery systems. Walzon wants to know whether these changes...
To test Ho: p=0.35 versus Hy:p>0.35, a simple random sample of n = 200 individuals is obtained and x = 69 successes are observed. (a) What does it mean to make a Type Il error for this test? (b) If the researcher decides to test this hypothesis at the a = 0.01 level of significance, compute the probability of making a Type II error, B, if the true population proportion is 0.38. What is the power of the test? (c)...