Elementary Statistics: Picturing the World (6th Edition)
6th Edition
ISBN: 9780321911216
Author: Ron Larson, Betsy Farber
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 8.2, Problem 4E
(a)
To determine
To find: The critical values when the population variances are equal.
(b)
To determine
To find: The critical values when the population variances are not equal.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
In Exercises 11 –14, test the claim about the difference between two population means u1 and u2 at the level of significance a. Assume the samples are random and independent, and the populations are normally distributed.
Following are the protein contents measured in two types of species:Species 1: 0.72 1.12 0.81 0.89 0.72 0.81 1.01 0.75 0.83Species 2: 1.21 0.93 0.80 1.12 1.22 0.94 0.87
i) Assuming normality, test the hypothesis that the two species have the sameaverage protein contents by using 5-step hypothesis testing procedure at 5 %level of significance, and using the critical values approach.ii) Calculate the p-value of this test and make decision.iii) Write down the standard error of this test and calculate its numerical value ?
Let X1, ..., Xn be a sample from an Poisson population with parameter λ.(a) Find the maximum likelihood estimator for λ.(b) Is the estimator unbiased?(c) Is the estimator consistent?
Chapter 8 Solutions
Elementary Statistics: Picturing the World (6th Edition)
Ch. 8.1 - Prob. 1TYCh. 8.1 - Prob. 2TYCh. 8.1 - Prob. 3TYCh. 8.1 - What is the difference between two samples that...Ch. 8.1 - Explain how to perform a two-sample z-test for the...Ch. 8.1 - Describe another way you can perform a hypothesis...Ch. 8.1 - What conditions are necessary in order to use the...Ch. 8.1 - Prob. 5ECh. 8.1 - Prob. 6ECh. 8.1 - Independent and Dependent Samples In Exercises 58,...
Ch. 8.1 - Prob. 8ECh. 8.1 - In Exercises 9 and 10, use the TI-H4 Plus display...Ch. 8.1 - Prob. 10ECh. 8.1 - Prob. 11ECh. 8.1 - In Exercises 1114, test the claim about the...Ch. 8.1 - In Exercises 1114, test the claim about the...Ch. 8.1 - Prob. 14ECh. 8.1 - Prob. 15ECh. 8.1 - Prob. 16ECh. 8.1 - Prob. 17ECh. 8.1 - Prob. 18ECh. 8.1 - Prob. 19ECh. 8.1 - Prob. 20ECh. 8.1 - Prob. 21ECh. 8.1 - Prob. 22ECh. 8.1 - Prob. 23ECh. 8.1 - Prob. 24ECh. 8.1 - Prob. 25ECh. 8.1 - Getting at the Concept Explain why the null...Ch. 8.1 - Prob. 27ECh. 8.1 - Prob. 28ECh. 8.1 - Prob. 29ECh. 8.1 - Prob. 30ECh. 8.2 - Prob. 1TYCh. 8.2 - Prob. 2TYCh. 8.2 - What conditions are necessary in order to use the...Ch. 8.2 - Explain how to perform a two-sample t-test for the...Ch. 8.2 - Prob. 3ECh. 8.2 - Prob. 4ECh. 8.2 - Prob. 5ECh. 8.2 - Prob. 6ECh. 8.2 - In Exercises 38, use Table 5 in Appendix B to find...Ch. 8.2 - Prob. 8ECh. 8.2 - In Exercises 912, test the claim about the...Ch. 8.2 - Prob. 10ECh. 8.2 - Prob. 11ECh. 8.2 - In Exercises 912, test the claim about the...Ch. 8.2 - Prob. 13ECh. 8.2 - Testing the Difference Between Two Means in...Ch. 8.2 - Prob. 15ECh. 8.2 - Testing the Difference Between Two Means in...Ch. 8.2 - Prob. 17ECh. 8.2 - Prob. 18ECh. 8.2 - Prob. 19ECh. 8.2 - Prob. 20ECh. 8.2 - Testing the Difference Between Two Means in...Ch. 8.2 - Prob. 22ECh. 8.2 - Constructing Confidence Intervals for 1 2 When...Ch. 8.2 - Prob. 24ECh. 8.2 - Prob. 25ECh. 8.2 - Prob. 26ECh. 8.2 - How Protein Affects Weight Gain in Overeaters In a...Ch. 8.2 - Prob. 2CSCh. 8.2 - How Protein Affects Weight Gain in Overeaters In a...Ch. 8.2 - Prob. 4CSCh. 8.2 - Prob. 5CSCh. 8.3 - Prob. 1TYCh. 8.3 - Prob. 2TYCh. 8.3 - Prob. 1ECh. 8.3 - Prob. 2ECh. 8.3 - Prob. 3ECh. 8.3 - Prob. 4ECh. 8.3 - Prob. 5ECh. 8.3 - Prob. 6ECh. 8.3 - Prob. 7ECh. 8.3 - Prob. 8ECh. 8.3 - Prob. 9ECh. 8.3 - Testing the Difference Between Two Means In...Ch. 8.3 - Prob. 11ECh. 8.3 - Prob. 12ECh. 8.3 - Prob. 13ECh. 8.3 - Prob. 14ECh. 8.3 - Prob. 15ECh. 8.3 - Prob. 16ECh. 8.3 - Testing the Difference Between Two Means In...Ch. 8.3 - Prob. 18ECh. 8.3 - Testing the Difference Between Two Means In...Ch. 8.3 - Prob. 20ECh. 8.3 - Prob. 21ECh. 8.3 - Prob. 22ECh. 8.3 - Prob. 23ECh. 8.3 - Prob. 24ECh. 8.4 - Prob. 1TYCh. 8.4 - Prob. 2TYCh. 8.4 - What conditions are necessary in order to use the...Ch. 8.4 - Explain how to perform a two-sample z-test for the...Ch. 8.4 - In Exercises 36, determine whether a normal...Ch. 8.4 - Prob. 4ECh. 8.4 - Prob. 5ECh. 8.4 - In Exercises 36, determine whether a normal...Ch. 8.4 - Prob. 7ECh. 8.4 - Prob. 8ECh. 8.4 - Prob. 9ECh. 8.4 - Prob. 10ECh. 8.4 - Prob. 11ECh. 8.4 - Prob. 12ECh. 8.4 - Prob. 13ECh. 8.4 - Prob. 14ECh. 8.4 - Prob. 15ECh. 8.4 - Prob. 16ECh. 8.4 - Prob. 17ECh. 8.4 - Prob. 18ECh. 8.4 - Prob. 19ECh. 8.4 - Prob. 20ECh. 8.4 - Prob. 21ECh. 8.4 - Prob. 22ECh. 8 - Medical research often involves blind and...Ch. 8 - Prob. 8.1.1RECh. 8 - Prob. 8.1.2RECh. 8 - Sample 1: The fuel efficiencies of 20 sports...Ch. 8 - Prob. 8.1.4RECh. 8 - Prob. 8.1.5RECh. 8 - In Exercises 58, test the claim about the...Ch. 8 - Prob. 8.1.7RECh. 8 - In Exercises 58, test the claim about the...Ch. 8 - Prob. 8.1.9RECh. 8 - Prob. 8.1.10RECh. 8 - Prob. 8.2.11RECh. 8 - Prob. 8.2.12RECh. 8 - Prob. 8.2.13RECh. 8 - Prob. 8.2.14RECh. 8 - Prob. 8.2.15RECh. 8 - Prob. 8.2.16RECh. 8 - Prob. 8.2.17RECh. 8 - Prob. 8.2.18RECh. 8 - Prob. 8.3.19RECh. 8 - In Exercises 1922, test the claim about the mean...Ch. 8 - Prob. 8.3.21RECh. 8 - Prob. 8.3.22RECh. 8 - Prob. 8.3.23RECh. 8 - Prob. 8.3.24RECh. 8 - Prob. 8.4.25RECh. 8 - Prob. 8.4.26RECh. 8 - Prob. 8.4.27RECh. 8 - Prob. 8.4.28RECh. 8 - Prob. 8.4.29RECh. 8 - Prob. 8.4.30RECh. 8 - Prob. 1CQCh. 8 - Prob. 2CQCh. 8 - Prob. 3CQCh. 8 - Prob. 4CQCh. 8 - Prob. 1CTCh. 8 - Prob. 2CTCh. 8 - Prob. 3CTCh. 8 - Prob. 4CTCh. 8 - Prob. 1RSRDCh. 8 - Prob. 2RSRDCh. 8 - Prob. 3RSRDCh. 8 - Prob. 4RSRDCh. 8 - Prob. 1TCh. 8 - Prob. 2TCh. 8 - Prob. 3TCh. 8 - Prob. 4TCh. 8 - Prob. 5TCh. 8 - Prob. 1CRCh. 8 - Prob. 2CRCh. 8 - Prob. 3CRCh. 8 - Prob. 4CRCh. 8 - In Exercises 36, construct the indicated...Ch. 8 - In Exercises 36, construct the indicated...Ch. 8 - Prob. 7CRCh. 8 - In Exercises 710, the statement represents a...Ch. 8 - In Exercises 710, the statement represents a...Ch. 8 - In Exercises 710, the statement represents a...Ch. 8 - In Exercises 710, the statement represents a...Ch. 8 - Prob. 12CRCh. 8 - Prob. 13CRCh. 8 - Prob. 14CRCh. 8 - Prob. 15CRCh. 8 - Prob. 16CRCh. 8 - Prob. 17CR
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- An urban community wants to show that the incidence of breast cancer is higher in their locality than in a neighboring rural area. (PCB levels were found to be higher in the soil of the urban community). If you find that in the urban community 20 out of 200 adult women have breast cancer and that in the rural community 10 out of 150 adult women have it, could you conclude, at a significance level of 0.05, that breast cancer is more prevalent in the urban community?1. The parameter of interest is:2. The hypotheses for this test are:3. The calculated test statistic is:4. The critical region is:5. Draw the critical region (make decision):6. It can be concluded that:arrow_forwarda. Assuming for the moment that all coefficients are significant, please interpret the coefficients of the four independent variables in the BIG b. To determine which of the two models above is statistically superior at the .10 level, please calculate the appropriate F‐statistic.arrow_forwardAssume that you have a sample of n1=8, with the sample mean X1=44, and a sample standard deviation of S1=5, and you have an independent sample of n2=14 from another population with a sample mean of X2=30 and the sample standard deviation S2=6. Using a significance level of α=0.025, what is the critical value for a one-tail test of the hypothesis H0: μ1≤ μ2 against the alternative H1: μ1>μ2? The critical value is ______ (Round to two decimal places as needed.)arrow_forward
- Testbank Question 9.37 Suppose you are testing the null hypothesis that a population mean is less than or equal to 46, against the alternative hypothesis that the population mean is greater than 46. If the sample size is 25, σ is known, and alpha = .01, the critical value of z is?arrow_forwardIn a survey of 460 drivers from the South, 397 wear a seat belt. In a survey of 340 drivers from the Northeast, 281 wear a seat belt. At alpha equals 0.06 , can you support the claim that the proportion of drivers who wear seat belts is greater in the South than in the Northeast? Assume the random samples are independent. Complete parts (a) through (e).arrow_forward2.Test the hypothesis that the average content of containers of a particular lubricant is 10 liters if the contents of a random sample of 10 containers are 10.1, 9.9, 10.2, 10.3, 10.3, 9.7, 9.8, 10.5, 10.2, and 9.8 liters. Use alpha 0.01 and assume that the distribution of content is normal.arrow_forward
- Given sample sizes n1 = n2 = 10, sample means = 5.2 and =7.1, and sample variances = 4 and = 6.2 using alpha = 0.05, test the hypothesis H0: u1 = u2 against Ha: u1 does not equal u2. A) What assumptions do we need to make about the data to use the central limit theorem? B) What is the value of the appropriate test statisctics?arrow_forwardChapter 6, Section 4-HT, Exercise 212 Use the t-distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from random samples, and if the sample sizes are small, assume the underlying distributions are relatively normal.Test H0 : μT=μC vs Ha : μT<μC using the fact that the treatment group (T) has a sample mean of 8.6 with a standard deviation of 4.1 while the control group (C) has a sample mean of 11.2with a standard deviation of 3.4. Both groups have 25 cases. (a) Give the test statistic and the p-value.Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places.test statistic = p-value = (b) What is the conclusion of the test at a 5% significance level? Reject H0. Do not reject H0.arrow_forwardConsider the following hypothesis statement using α=0.05 and data from two independent samples. Assume the population variances are equal and the populations are normally distributed. Complete parts a and b. H0: μ1−μ2≤11 x1=71.4 x2=58.5 H1: μ1−μ2>11 s1=19.9 s2=18.3 n1=15 n2=20 a. Calculate the appropriate test statistic and interpret the result. 1. The test statistic is 2. The critical value(s) is(are) b. . Identify the p-value from part a and interpret the result. 1.. Identify the p-value from part a and interpret the result.arrow_forward
- Consider the following hypothesis statement using α=0.01 and data from two independent samples. Assume the population variances are equal and the populations are normally distributed. Complete parts a and b. H0: μ1−μ2=0 x1=14.5 x2=13.0 H1: μ1−μ2≠0 s1=2.6 s2=3.3 n1=22 n2=15 a. Calculate the appropriate test statistic and interpret the result. The test statistic is? The critical value(s) is(are)? b. Identify the p-value from part a and interpret the result.arrow_forwardIn a test of H0: p = 0.8 against H1: p ≠ 0.8, a sample of size 1000 produces Z = 2.05 for the value of the test statistic. Thus the p-value (or observed level of significance) of the test is approximately equal to:arrow_forwardIn Exercises 5–20, assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. (Note: Answers in Appendix D include technology answers based on Formula 9-1 along with “Table” answers based on Table A-3 with df equal to the smaller of n1 − 1 and n2 − 1.) Car and Taxi Ages When the author visited Dublin, Ireland (home of Guinness Brewery employee William Gosset, who first developed the t distribution), he recorded the ages of randomly selected passenger cars and randomly selected taxis. The ages can be found from the license plates. (There is no end to the fun of traveling with the author.) The ages (in years) are listed below. We might expect that taxis would be newer, so test the claim that the mean age of cars is greater than the mean age of taxis.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman
Statistics 4.1 Point Estimators; Author: Dr. Jack L. Jackson II;https://www.youtube.com/watch?v=2MrI0J8XCEE;License: Standard YouTube License, CC-BY
Statistics 101: Point Estimators; Author: Brandon Foltz;https://www.youtube.com/watch?v=4v41z3HwLaM;License: Standard YouTube License, CC-BY
Central limit theorem; Author: 365 Data Science;https://www.youtube.com/watch?v=b5xQmk9veZ4;License: Standard YouTube License, CC-BY
Point Estimate Definition & Example; Author: Prof. Essa;https://www.youtube.com/watch?v=OTVwtvQmSn0;License: Standard Youtube License
Point Estimation; Author: Vamsidhar Ambatipudi;https://www.youtube.com/watch?v=flqhlM2bZWc;License: Standard Youtube License