For a hypothesis test with a probability of a Type II error of 60% and a probability of a Type I error of 5%, which of the following statements is most accurate? A. The power of the test is 40%, and there is a 5% probability that the test statistic will exceed the critical value(s). B. There is a 95% probability that the test statistic will be between the critical values if this is a two tailed test. C. There is a 5% probability that the null hypothesis will be rejected when actually true, and the probability of rejecting the null when it is false is 40%.

For a hypothesis test with a probability of a Type II error of 60% and a probability of a Type I error of 5%, which of the following statements is most accurate? A. The power of the test is 40%, and there is a 5% probability that the test statistic will exceed the critical value(s). B. There is a 95% probability that the test statistic will be between the critical values if this is a two tailed test. C. There is a 5% probability that the null hypothesis will be rejected when actually true, and the probability of rejecting the null when it is false is 40%.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

When one changes the significance level of a hypothesis test from 0.10 to 0.05, which of the following will happen? Check all that apply. A. The chance that the null hypothesis is true changes from 0.10 to 0.05. OB. The test becomes less stringent to reject the null hypothesis (i.e. it becomes easier to reject the null hypothesis). c. It becomes harder to prove that the null hypothesis is true. OD. The chance of committing a Type I error changes from 0.10 to 0.05. ⒸE. The chance of committing a Type II error changes from 0.10 to 0.05. OF. It becomes easier to prove that the null hypothesis is true. ⒸG. The test becomes more stringent to reject the null hypothesis (i.e., it becomes harder to reject the null hypothesis).
If your null and alternative hypothesis are:H0:p=0.78 H1:p<0.78Then the test is: two tailed right tailed left tailed
Suppose Connie owns a pet store in a large community that has over 50,000 pet owners. She believes that the proportion of men who own cats is different from the proportion of women who own cats. Connie decides to test this claim by performing a two-sample ?-test for two proportions. Her hypotheses are given by ?0:??=???1:??≠?? where ?0 is the null hypothesis, and ?1 is the alternative hypothesis. The variables ?? and ?? represents the population proportion of men and women cat owners, respectively. She randomly samples 420 men and 493 women who are pet owners in the community and finds that 234 men own cats and 256 women own cats. Determine the pooled sample proportion, ?̂. Provide your answer precise to three decimal places. Compute the standard error of the difference of the sample proportions (SE). Provide your answer precise to three decimal places. SE = ?̂=
Many Americans believe that women talk more than men. A 1998 study tested this theory by evaluating the number of words spoken daily by men and women. The researcher of the study conducted a two-sample ?t‑test set at a signficance level of α=0.05. The null and alternative hypotheses, ?0 and ?1, are ?0:?M≥?W ?1:?M<?W where ?M represents the mean number of words spoken per day by men, and ?W represents the mean number of words spoken per day by women. The researcher randomly selected 20 men and 27 women and tracked the number of words spoken per day by each individual over a period of time. The sample results are summarized in the table. Population Samplesize Sample mean(words) Sample standarddeviation (words) Men ?M=20 x¯M=12867 ?M=8343 Women ?W= 27 x¯W=16496 ?W=7914 The population variances are unknown and assumed to be unequal. The Welch–Satterthwaite approximation of the degrees of freedom for this test is 39.8360. Assume the conditions for a two‑sample ?t‑test are…
a. What are the null and alternative hypotheses? b. The test statistic, t, is c. The P-value is d. State the conclusion for the test. e. Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean.
Suppose the present success rate in the treatment of a particular psychiatric disorder for the relevant population is known to be .73 (73%). A research group hopes to demonstrate that the success rate of a new treatment will be better than this standard. Use the letter p to represent the success rate of the new treatment. Write null and alternative hypotheses for p. Ho: p|? v H2: p? v a
In testing hypotheses, which of the following would be strong evidence against the null hypothesis?a. Obtaining data with a test statistic of small magnitude.b. Obtaining data with a small P-value.c. Obtaining data with a large P-value.d. Using a large level of significance, α.e. Using a small level of significance, α
An educational psychologist studies the effect of frequent testing on retention of class material. In one of the professor's sections, students are given quizzes each week. The second section receives only two tests during the semester. At the end of the semester, both sections receive the same final exam, and the scores are summarized below. Do the data indicate that testing frequency has a significant effect on performance? Use a two-tailed test with α = .01. Include the null hypothesis in symbols, critical region(s), and a conclusion about significance. Compute r2 and state the size of the effect (e.g. small, medium, large). Frequent Quizzes Two Exams n = 15 n = 15 M = 72 SS= 112 M = 68 SS= 98
Consider the following statements: I. As far as the probability of a Type I error is concerned, a two-tailed hypothesis test is more accurate than a one-tailed hypothesis test. II. A point estimation procedure in a one sample scenario utilizes information in a sample to arrive at two points, one positive and one negative in order to estimate the population parameter of interest. a. I and II are both true. b. I and II are both false. c. I is true and II is false. d. I is false and II is true. e. I is false and II is sometimes true.
Suppose a 95% confidence interval for the difference in test scores between Class 1 and Class 2 (in that order) is the following: 9 +/− 2. These results were based on independent samples of size 100 from each class. Now suppose you switch the order of Class 1 and Class 2 in your analysis but keep the data labeled correctly in terms of which class they came from. Which of the following statements is false? A) You can't do it this way. You'll get negative numbers for the difference in the means and/or negative numbers for the standard error. B) You are confident that the average for Class 2 is 7 to 11 points lower than for Class 1. C) You are still confident that the classes have significantly different mean scores. D) Your 95% confidence interval will now be entirely negative: from −7 to −11.
Males and females were asked what they would do if they received a $100 bill in the mail that was addressed to their neighbor, but had been incorrectly delivered to them. Of the 70 males sampled, 55 said yes they would return it to their neighbor. Of the 130 females sampled, 120 said yes. The overall question is: Is this sufficient evidence to say that the two true proportions are different? Assume that the p-value turns out to be .027 (again not the correct p-value for this situation but use it to answer this question). What is your decision on this hypothesis test using a 5% level of significance? O Fail to reject the null hypothesis Reject the null hypothesis
You wish to test the following claim (H.) at a significance level of a = 0.005. You believe both populations are normally distributed, but you do not know the standard deviations for either. And you have no reason to believe the variances of the two populations are equal You obtain a sample - 19.1 from the first population. 7.1 from of size ni 23 with a mean of a1 You obtain a sample of size n2 the second population. 86.6 and a standard deviation of s1 20 with a mean of r2 96.5 and a standard deviation of s2 = a. What is the test statistic for this sample? test statistic = Round to 3 decimal places. b. What is the p-value for this sample? For this calculation, use p-value Use Technology Round to 4 decimal places.