(d) Suppose that the union decides to perform another statistical test using the samepopulation, the same null and alternative hypotheses, and the same sample size,but for this second test the union uses a significance level of 0.01 instead of asignificance level of 0.10. Assuming that the actual value of u is $7.82, how doesthe probability that the union commits a Type II error in this second test compareto the probability that the union commits a Type II error in the original test?O The probability of committing a Type II error in the second test is greaterO The probability of committing a Type II error in the second test is lessO The probabilities of committing a Type II error are equal A union of restaurant and foodservice workers would like to estimate this year's mean hourly wage u for foodservice workers in the U.S. Last year's mean hourlywage was $8.08, and there is good reason to believe that this year's value is less than last year's. The union decides to do a statistical test to see if it can beconcluded that the mean has decreased. The union chooses a random sample of 75 wages from this year.Suppose that the population of hourly wages of foodservice workers in the U.S. has a standard deviation of $1.25 and that the union performs its hypothesistest using the 0.10 level of significance.Based on this information, answer the questions below. Carry your intermediate computations to four or more decimal places, and round your responses asindicated.(If necessary, consult a list of formulas.)(a) What are the null hypothesis Ho and the alternative hypothesis H, that the unionshould use for the test?Ho: DH₁: 0(b) Assuming that the actual value of μ is $7.82, what is the probability that the unionrejects the null hypothesis? Round your response to two or more decimal places.(c) What is the probability that the union rejects the null hypothesis when, in fact, it istrue? Round your response to two or more decimal places.(d) Suppose that the union decides to perform another statistical test using the samepopulation, the same null and alternative hypotheses, and the same sample size,but for this second test the union uses a significance level of 0.01 instead of aμX90=0aXS00OSO□□ 0<0РO

This question is related to hypothesis testing and probability of committing a Type II error. The…

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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...

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A two-tailed test is performed at the 0.10 level of significance. The p-value is determined to be 0.03. The null hypothesis O should not be rejected. has been designed incorrectly. O must be rejected. could be rejected, depending on the sample size.
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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.
A. Suppose we want to test whether or not three means are equal. We want to perform this test with a 8% significance level.If we perform an ANOVA test, what is the probability of the test producing accurate results (avoiding a Type I error)? B. Suppose we, instead, run three separate hypothesis tests (t-tests), each with 8% significance level. Mean 1 = Mean 2Mean 1 = Mean 3Mean 2 = Mean 3What is the probability that all three tests would be accurate? C. Why is an ANOVA test more accurate than 3 different tests?
Test the claim that the mean GPA of night students is larger than 2.3 at the .025 significance level. The null and alternative hypothesis would be: Но : р — 2.3 Но:н — 2.3 Но:р %3D 0.575 Но: д —— 2.3 Но:р %3D 0.575 Но:р 3 0.575 H:р + 2.3 Hi:p 2.3 Н:р#0.575 H:р> 0.575 The test is: left-tailed right-tailed two-tailed Based on a sample of 65 people, the sample mean GPA was 2.34 with a standard deviation of 0.06 The test statistic is: (to 2 decimals) The critical value is: (to 2 decimals) Based on this we: O Fail to reject the null hypothesis O Reject the null hypothesis
Two different simple random samples are drawn from two different populations. The first sample consists of 20 people with 10 having a common attribute. The second sample consists of 2200 people with 1597 of them having the same common attribute. Compare the results from a hypothesis test of p1= p2 (with a 0.01 significance level) and a 99% confidence interval estimate of p1− p2.
An economist is studying salaries for high technology companies and wants to test the claim that the average salary for high tech employees is less than $70,000. The economist selects a sample of 35 random employees from various high tech companies and records their salaries. Based on past studies, the economist determines that the population standard deviation is $8,500. The economist conducts a one-mean hypothesis test at the 5% significance level to test the claim that the average salary for high tech employees is less than $70,000. Which is the correct setup for the null and alternative hypothesis for this example? Select the correct answer below: H0:μ=70,000; Ha:μ<70,000, which is a left-tailed test. H0:μ=70,000; Ha:μ>70,000, which is a right-tailed test H0:μ<70,000; Ha:μ=70,000, which is a left-tailed test. H0:μ>70,000; Ha:μ=70,000, which is a left-tailed test.
Two different simple random samples are drawn from two different populations. The first sample consists of 30 people with 16 having a common attribute. The second sample consists of 2000 people with 1409 of them having the same common attribute. Compare the results from a hypothesis test of p, = p2 (with a 0.01 significance level) and a 99% confidence interval estimate of p, -P2. O A. Ho: P1 SP2 H1: P1 #P2 O B. Ho: P1 *P2 H1: P1 = P2 OC. Ho: P1 = P2 H1: P, > P2 O D. Ho: P1 2 P2 H: P1 +P2 O E. Ho: P1 = P2 H:P1 #P2 OF. Ho: P1 =P2 H;: P1
Two different simple random samples are drawn from two different populations. The first sample consists of 40 people with 20 having a common attribute. The second sample consists of 1800 people with 1291 of them having the same attribute. Compare the results from a hypothesis test p1=p2 (with a 0.05 significance level) and a 95% confidence interval estimate of p1-p2. What are the null and alternative hypotheses for the hypothesis test?
A new treatment for a certain disease is claimed to be effective in more than 80 % of cases . To test this claim the treatment was given to 100 randomly selected patients . The treatment was effective in 85 out of the 100 patients . What is the conclusion at a 5 % level of significance ? A. Reject the null hypothesis .There is sufficient evidence to claim that the treatment is effective in more than 80 % of cases B. Reject the null hypothesis .There is not sufficient evidence to claim that the treatment is effective in more than 80 % of cases C. Fail to reject the null hypothesis. There is sufficient evidence to claim that the treatment is effective in more than 80 % of cases D. Fail to reject the null hypothesis. There is not sufficient evidence to claim that the treatment is effective in more than 80 % of cases
A teacher is explaining to her class the concepts of genetics regarding eye color. She assumes that each category will have the same number of students in it. Use a 0.05 level of significance. Expected Eye Colors: All the categories of eye colors are the same. Here are the results for the class. Blue Green Green Hazel Brown Blue Green Brown Hazel Hazel Hazel Brown Blue Blue Blue Brown Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Question 25 Saved Listen What is the null hypothesis? Question 25 options: Ho: All the categories of eye colors are the same. Ho: At least one of the categories of eye colors is not the same. Question 26 Saved Listen What is the alternative hypothesis? Question 26 options: Ha: At least one of the categories of eye…
The value obtained for the test statistic, z, in a one-mean z-test is given. Whether the test is two tailed, left tailed, or right tailed is also specified. For parts (a) and (b), determine the P-value and decide whether, at the 1% significance level, the data provide sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis. a. The test statistic in a two-tailed test is z = -0.93. The P-value is (Round to three decimal places as needed.) ... sufficient evidence to reject the null hypothesis in favor of the significance level. At the 1% significance level, the data the alternative hypothesis because the obtained P-value is b. The test statistic in a two-tailed test is z = 0.61. The P-value is (Round to three decimal places as needed.) sufficient evidence to reject the null hypothesis in favor of the significance level. At the 1% significance level, the data the alternative hypothesis because the obtained P-value is Time Remaining: 01:57:58 Mand

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