Introduction to Statistics and Data Analysis
5th Edition
ISBN: 9781305115347
Author: Roxy Peck; Chris Olsen; Jay L. Devore
Publisher: Brooks Cole
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 10.5, Problem 64E
Optical fibers are used in telecommunications to transmit light. Suppose current technology allows production of fibers that transmit light about 50 km. Researchers are trying to develop a new type of glass fiber that will increase this distance. In evaluating a new fiber, it is of interest to test H0: μ = 50 versus Ha: μ > 50, with μ denoting the mean transmission distance for the new optical fiber.
- a. Assuming σ = 10 and n = 10, use Appendix Table 5 to approximate β, the
probability of a Type II error, for each of the given alternative values of μ for a test with significance level 0.05:- i. 52
- ii. 55
- iii. 60
- iv. 70
- b. What happens to β in each of the cases in Part (a) if σ is actually larger than 10? Explain your reasoning.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
The geoemetric mean of 2, 4 & 8.
Based on the image attached,
Select one:
a. V only
b. I and VI only
c. VI only
d. II and V only
Suppose the mean of Z is 2. What is the mean of Y if a = 1.22 and Y=aZ? (Use two decimal places, ex: 12.34)
Chapter 10 Solutions
Introduction to Statistics and Data Analysis
Ch. 10.1 - Explain why the statement x=50 is not a legitimate...Ch. 10.1 - For the following pairs, indicate which do not...Ch. 10.1 - To determine whether the pipe welds in a nuclear...Ch. 10.1 - Prob. 4ECh. 10.1 - Prob. 5ECh. 10.1 - Prob. 6ECh. 10.1 - Prob. 7ECh. 10.1 - A researcher speculates that because of...Ch. 10.1 - A county commissioner must vote on a resolution...Ch. 10.1 - A cruise ship charges passengers 3 for a can of...
Ch. 10.1 - Prob. 11ECh. 10.2 - Prob. 12ECh. 10.2 - Prob. 13ECh. 10.2 - Medical personnel are required to report suspected...Ch. 10.2 - Prob. 15ECh. 10.2 - A television manufacturer claims that (at least)...Ch. 10.2 - A manufacturer of hand-held calculators receives...Ch. 10.2 - Water specimens are taken from water used for...Ch. 10.2 - Suppose that for a particular hypothesis test, the...Ch. 10.2 - Suppose that you arc an inspector for the Fish and...Ch. 10.2 - Prob. 21ECh. 10.2 - An automobile manufacturer is considering using...Ch. 10.3 - Use the definition of the P-value to explain the...Ch. 10.3 - For which of the following P-values will the null...Ch. 10.3 - Prob. 25ECh. 10.3 - Let p denote the proportion of students at a...Ch. 10.3 - Assuming a random sample from a large population,...Ch. 10.3 - Prob. 28ECh. 10.3 - In a survey of 1000 women age 22 to 35 who work...Ch. 10.3 - The paper Debt Literacy, Financial Experiences and...Ch. 10.3 - "Most Like it Hot" is the title of a press release...Ch. 10.3 - In a survey of 1005 adult Americans, 46% indicated...Ch. 10.3 - Prob. 33ECh. 10.3 - Prob. 34ECh. 10.3 - Prob. 35ECh. 10.3 - Prob. 36ECh. 10.3 - Prob. 37ECh. 10.3 - The article Cops Get Screened for Digital Dirt...Ch. 10.3 - Refer back to the previous exercise. The actual...Ch. 10.3 - The report 2007 Electronic Monitoring ...Ch. 10.3 - Prob. 41ECh. 10.4 - Prob. 42ECh. 10.4 - Give as much information as you can about the...Ch. 10.4 - Paint used to paint lines on roads must reflect...Ch. 10.4 - A certain pen has been designed so that actual...Ch. 10.4 - Prob. 46ECh. 10.4 - The paper Playing Active Video Games Increases...Ch. 10.4 - Prob. 48ECh. 10.4 - Prob. 49ECh. 10.4 - Prob. 50ECh. 10.4 - Prob. 51ECh. 10.4 - Medical research has shown that repeated wrist...Ch. 10.4 - Prob. 53ECh. 10.4 - A comprehensive study conducted by the National...Ch. 10.4 - Prob. 55ECh. 10.4 - The paper titled Music for Pain Relief (The...Ch. 10.4 - Many consumers pay careful attention to stated...Ch. 10.4 - Much concern has been expressed regarding the...Ch. 10.5 - The power of a test is influenced by the sample...Ch. 10.5 - Prob. 60ECh. 10.5 - Let denote the mean lifetime (in hours) for a...Ch. 10.5 - The city council in a large city has become...Ch. 10.5 - The amount of shaft wear after a fixed mileage was...Ch. 10.5 - Optical fibers are used in telecommunications to...Ch. 10.5 - Prob. 65ECh. 10.6 - In 2006, Boston Scientific sought approval for a...Ch. 10.6 - The article Boy or Girl: Which Gender Baby Would...Ch. 10 - Prob. 68CRCh. 10 - In a national survey of 2013 adults, 1590...Ch. 10 - Students at the Akademia Podlaka conducted an...Ch. 10 - Prob. 71CRCh. 10 - Prob. 72CRCh. 10 - A number of initiatives on the topic of legalized...Ch. 10 - Prob. 74CRCh. 10 - Prob. 75CRCh. 10 - Prob. 76CRCh. 10 - Prob. 77CRCh. 10 - Duck hunting in populated areas faces opposition...Ch. 10 - Past experience has indicated that the response...Ch. 10 - An automobile manufacturer who wishes to advertise...Ch. 10 - A student organization uses the proceeds from a...Ch. 10 - A hot tub manufacturer advertises that with its...Ch. 10 - Prob. 1CRECh. 10 - Prob. 2CRECh. 10 - Prob. 3CRECh. 10 - Prob. 4CRECh. 10 - Prob. 5CRECh. 10 - The article Should Canada Allow Direct-to-Consumer...Ch. 10 - Prob. 7CRECh. 10 - It probably wouldnt surprise you to know that...Ch. 10 - The article Doctors Cite Burnout in Mistakes (San...Ch. 10 - The National Geographic Society conducted a study...Ch. 10 - Heinz Plays Catch-up After Under-Filling Ketchup...Ch. 10 - In a survey conducted by Yahoo Small Business,...Ch. 10 - In an AP-AOL sports poll (Associated Press,...Ch. 10 - Prob. 14CRECh. 10 - A survey of teenagers and parents in Canada...Ch. 10 - The same survey referenced in the previous...
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
- Find the mean hourly cost when the cell phone described above is used for 240 minutes.arrow_forwardUse theorem 5.4.2 to form a proportion in which SV is a geometric mean. Hint: SVTRVS Exercises 1-6arrow_forwardPlanetary Velocity The following table gives the mean velocity of planets in their orbits versus their mean distance from the sun. Note that 1AU astronomical unit is the mean distance from Earth to the sun, abut 93 million miles. Planet d=distance AU v=velocity km/sec Mercury 0.39 47.4 Venus 0.72 35.0 Earth 1.00 29.8 Mars 1.52 24.1 Jupiter 5.20 13.1 Saturn 9.58 9.7 Uranus 19.20 6.8 Neptune 30.05 5.4 Astronomers tell us that it is reasonable to model these data with a power function. a Use power regression to express velocity as a power function of distance from the sun. b Plot the data along with the regression equation. c An asteroid orbits at a mean distance of 3AU from the sun. According to the power model you found in part a, what is the mean orbital velocity of the asteroid?arrow_forward
- "Durable press" cotton fabrics are treated to improve their recovery from wrinkles after washing. "Wrinkle recovery angle" measures how well a fabric recovers from wrinkles. Higher is better. Here are data on the wrinkle recovery angle (in degrees) for the same fabric specimens discussed in the previous exercise: Permafresh Hylite 156 148 152 197 151 187 122 142 133 A manufacturer wants to know how large is the difference in mean wrinkle recovery angle. a. The mean and the standard deviation for the Permafresh are: Round to 3 decimal places. Round to 3 decimal places. b. The mean and the standard deviation for the Hylite are: Round to 3 decimal places. Round to 3 decimal places. c. The standard error is: SE = Round to 3 decimal places. The critical value from the distribution for a confidence interval of 99.8% is: t= Use degrees of freedom of 3. Use Technology. Round to 3 decimal places. d. Using the the answer from above (all rounded to 3 decimal places), calculate by hand a 99.8%…arrow_forwardPart Darrow_forwardA survey is carried out at a university to estimate the percentage of undergraduates living at home during the current term. What is the population? the parameter?arrow_forward
- The following table gives the mean velocity of planets in their orbits versus their mean distance from the sun. Note that 1 AU (astronomical unit) is the mean distance from Earth to the sun, about 93 million miles. Planet d = distance (AU) v = velocity (km/sec) Mercury 0.39 47.4 Venus 0.72 35.0 Earth 1 29.8 Mars 1.52 24.1 Jupiter 5.20 13.1 Saturn 9.58 9.7 Uranus 19.20 6.8 Neptune 30.05 5.4 Astronomers tell us that it is reasonable to model these data with a power function. (a) Use power regression to express velocity as a power function of distance from the sun. (Round regression parameters to two decimal places.) V = 21.41 x d -0.50 V = 21.41 x d-0.29 ° v = 29.73 x d¬0.50 V = 29.73 x d-0.73 v = 29.73 x d0.50 (b) Plot the data along with the regression equation. v V 50 50 H 50 50H 40 40 40 40 30 30 30 30 20 20 20 20- 10 10 10 10 d 10 15 20 25 30 d d 5 10 15 20 25 30 5 10 15 20 25 30 5 10 15 20 25 30 (c) An asteroid orbits at a mean distance of 3 AU from the sun. According to the power…arrow_forwardAn article reported the following frequencies with which ethnic characters appeared in recorded commercials that aired on Philadelphia television stations. Ethnicity: Frequency: African American USE SALT Calculate th x² = | OHP₁ P₂P, P = 0.250 H₁: at least one p, = 0.25 Asian In a recent census, the proportions for these four ethnic groups are 0.177, 0.042, 0.734, and 0.047, respectively. Does the data suggest that the proportions in commercials are different from the census proportions? Carry out a test of appropriate hypotheses using a significance level of 0.01. (Let P P₂P and p be the population proportions of the four ethnic groups (African American, Asian, Caucasian, and Hispanic respectively) appearing in commercials on Philadelphia television stations.) State the appropriate hypotheses. O H₂: P₁ = 0.047, P₂ -0.011, p = 0.330, p = 0.005 H: at least one p, P Caucasian Hispanic 330 OH: P₁ = 0.120, P, = 0.028, p = 0.840, p = 0.013 H: at least one p, * P OH₂: P₁ = 0.177, P₂ = 0.042,…arrow_forwardA line’s length has been measured repeatedly on different occasions. The following are the results obtained: 1st measurement record = 352.33 ± 0.03cm 2nd measurement record = 351.79 ± 0.07cm 3rd measurement record = 352.16 ± 0.08cm 4th measurement record = 352.84 ± 0.01cm 5th measurement record = 351.55 ± 0.04cm Determine the weighted mean of the 5 sets of measurements. Given the computed weighted mean of the measurements, what is the relative precision if the true length of the line is 352.39cm.arrow_forward
- "Durable press" cotton fabrics are treated to improve their recovery from wrinkles after washing. "Wrinkle recovery angle" measures how well a fabric recovers from wrinkles. Higher is better. Here are data on the wrinkle recovery angle (in degrees) for the same fabric specimens discussed in the previous exercise: Permafresh Hylite 106 165 126 171 155 142 153 187 117 A manufacturer wants to know how large is the difference in mean wrinkle recovery angle. The mean and the standard deviation for the Permafresh are: ¯x= s= Round to 3 decimal places. 2. The mean and the standard deviation for the Hylite are: ¯x= s= Round to 3 decimal places. 3.The standard error is: SE = ________ Round to 3 decimal places. The critical value from the distribution for a confidence interval of 98% is: t*= ________Use degrees of freedom of 3. Use Technology Round to 3 decimal places. Using the the answer from above (all rounded to 3 decimal places), calculate by hand a 98%…arrow_forwardWhat is the approximate forecast for May using a four-month moving average? Nov. Dec. Jan. Feb. Mar. Apni. 39 36 40 42 46 46 OA 44 OB.3 OC42 O D.43arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
The Shape of Data: Distributions: Crash Course Statistics #7; Author: CrashCourse;https://www.youtube.com/watch?v=bPFNxD3Yg6U;License: Standard YouTube License, CC-BY
Shape, Center, and Spread - Module 20.2 (Part 1); Author: Mrmathblog;https://www.youtube.com/watch?v=COaid7O_Gag;License: Standard YouTube License, CC-BY
Shape, Center and Spread; Author: Emily Murdock;https://www.youtube.com/watch?v=_YyW0DSCzpM;License: Standard Youtube License