Mathematical Statistics with Applications
7th Edition
ISBN: 9781111798789
Author: Dennis O. Wackerly
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 10.3, Problem 30E
To determine
Delineate how small would the sample percentage needed before the claim could be proved false.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
If a researcher obtains a sample mean of M= 54, from a population with u = 46. With a given alpha, which combination of factors is most likely to result in rejecting the null hypothesis?
A manufacturer of hand-held calculators receives large shipments of printed circuits from a supplier. It is too costly and time-consuming to inspect all incoming circuits, so when each shipment arrives, a sample is selected for inspection. Information from the sample is then used to test
H0: p = 0.01
versus
Ha: p > 0.01,
where p is the actual proportion of defective circuits in the shipment.
If the null hypothesis is not rejected, the shipment is accepted, and the circuits are used in the production of calculators. If the null hypothesis is rejected, the entire shipment is returned to the supplier because of inferior quality. (A shipment is defined to be of inferior quality if it contains more than 1% defective circuits.)
In this context, define Type I and Type II errors. (Select all that apply.)
a. A Type I error is obtaining convincing evidence that more than 1% of a shipment is defective when in fact (at most) 1% of the shipment is defective.
b. A Type I error is not…
A company selling home furnaces claims that installingtheir new high efficiency furnace will “cut your heating
bill in half.” A consumer agency collects data for a ran-dom sample of homes and plots this year’s heating costs
with the new furnaces against previous costs with the oldfurnaces. Which are the most appropriate hypotheses totest the company’s claim?A) H0: b = 0, HA: b ≠ 0B) H0: b = 0, HA: b 7 0C) H0: b = 0, HA: b 6 0D) H0: b = 0, HA: b 6 0.5E) H0: b = 0.5, HA: b ≠ 0.5
Chapter 10 Solutions
Mathematical Statistics with Applications
Ch. 10.2 - Define and for a statistical test of hypotheses.Ch. 10.2 - An experimenter has prepared a drug dosage level...Ch. 10.2 - Refer to Exercise 10.2. a Find the rejection...Ch. 10.2 - Suppose that we wish to test the null hypothesis...Ch. 10.2 - Let Y1 and Y2 be independent and identically...Ch. 10.2 - We are interested in testing whether or not a coin...Ch. 10.2 - True or False Refer to Exercise 10.6. a The level...Ch. 10.2 - A two-stage clinical trial is planned for testing...Ch. 10.3 - A survey published in the American Journal of...Ch. 10.3 - The hourly wages in a particular industry are...
Ch. 10.3 - The output voltage for an electric circuit is...Ch. 10.3 - The Rockwell hardness index for steel is...Ch. 10.3 - Shear strength measurements derived from...Ch. 10.3 - Prob. 22ECh. 10.3 - Studies of the habits of white-tailed deer...Ch. 10.3 - A study by Childrens Hospital in Boston indicates...Ch. 10.3 - An article in American Demographics reports that...Ch. 10.3 - According to the Washington Post, nearly 45% of...Ch. 10.3 - The state of California is working very hard to...Ch. 10.3 - Prob. 28ECh. 10.3 - Prob. 29ECh. 10.3 - Prob. 30ECh. 10.3 - Prob. 31ECh. 10.3 - In March 2001, a Gallup poll asked. How would you...Ch. 10.3 - A political researcher believes that the fraction...Ch. 10.3 - Exercise 8.58 stated that a random sample of 500...Ch. 10.3 - Michael Sosin investigated determinants that...Ch. 10.3 - Prob. 36ECh. 10.4 - Refer to Exercise 10.19. If the voltage falls as...Ch. 10.4 - Refer to Exercise 10.20. The steel is sufficiently...Ch. 10.4 - Refer to Exercise 10.30. Calculate the value of ...Ch. 10.4 - Refer to Exercise 10.33. The political researcher...Ch. 10.4 - Refer to Exercise 10.34. Using the rejection...Ch. 10.4 - In Exercises 10.34 and 10.41, how large should the...Ch. 10.4 - A random sample of 37 second graders who...Ch. 10.4 - Refer to Exercise 10.43. Find the sample sizes...Ch. 10.5 - Refer to Exercise 10.21. Construct a 99%...Ch. 10.5 - Prob. 46ECh. 10.5 - Prob. 47ECh. 10.5 - Prob. 48ECh. 10.5 - Prob. 49ECh. 10.6 - High airline occupancy rates on scheduled flights...Ch. 10.6 - Two sets of elementary schoolchildren were taught...Ch. 10.6 - A biologist has hypothesized that high...Ch. 10.6 - How would you like to live to be 200 years old?...Ch. 10.6 - Do you believe that an exceptionally high...Ch. 10.6 - A check-cashing service found that approximately...Ch. 10.6 - Prob. 56ECh. 10.6 - Prob. 57ECh. 10.6 - Prob. 58ECh. 10.8 - Why is the Z test usually inappropriate as a test...Ch. 10.8 - Prob. 62ECh. 10.8 - A chemical process has produced, on the average,...Ch. 10.8 - A coin-operated soft-drink machine was designed to...Ch. 10.8 - Operators of gasoline-fueled vehicles complain...Ch. 10.8 - Researchers have shown that cigarette smoking has...Ch. 10.8 - Nutritional information provided by Kentucky Fried...Ch. 10.8 - Prob. 68ECh. 10.8 - Two methods for teaching reading were applied to...Ch. 10.8 - A study was conducted by the Florida Game and Fish...Ch. 10.8 - Under normal conditions, is the average body...Ch. 10.8 - Prob. 72ECh. 10.8 - In Exercise 8.83, we presented some data collected...Ch. 10.8 - Prob. 74ECh. 10.8 - Prob. 75ECh. 10.8 - Prob. 76ECh. 10.8 - Prob. 77ECh. 10.9 - A manufacturer of hard safety hats for...Ch. 10.9 - Prob. 79ECh. 10.9 - Prob. 80ECh. 10.9 - Prob. 81ECh. 10.9 - Exercises 8.83 and 10.73 presented some data...Ch. 10.9 - Prob. 83ECh. 10.9 - An experiment published in The American Biology...Ch. 10.9 - Prob. 85ECh. 10.9 - Aptitude tests should produce scores with a large...Ch. 10.9 - Prob. 87ECh. 10.10 - Refer to Exercise 10.2. Find the power of the test...Ch. 10.10 - Prob. 89ECh. 10.10 - Refer to Exercise 10.5. a Find the power of test 2...Ch. 10.10 - Let Y1, Y2,, Y20 be a random sample of size n = 20...Ch. 10.10 - Consider the situation described in Exercise...Ch. 10.10 - For a normal distribution with mean and variance...Ch. 10.10 - Suppose that Y1, Y2, ,Yn constitute a random...Ch. 10.10 - Prob. 95ECh. 10.10 - Prob. 96ECh. 10.10 - Prob. 97ECh. 10.10 - Prob. 98ECh. 10.10 - Prob. 99ECh. 10.10 - Prob. 100ECh. 10.10 - Prob. 101ECh. 10.10 - Prob. 102ECh. 10.10 - Prob. 103ECh. 10.10 - Refer to the random sample of Exercise 10.103. a...Ch. 10.11 - Let Y1, Y2,, Yn denote a random sample from a...Ch. 10.11 - A survey of voter sentiment was conducted in four...Ch. 10.11 - Prob. 107ECh. 10.11 - Prob. 108ECh. 10.11 - Let X1, X2,, Xm denote a random sample from the...Ch. 10.11 - Show that a likelihood ratio test depends on the...Ch. 10.11 - Suppose that we are interested in testing the...Ch. 10.11 - Prob. 112ECh. 10.11 - Refer to Exercise 10.112. Show that in testing of...Ch. 10.11 - Prob. 114ECh. 10 - True or False. a If the p-value for a test is...Ch. 10 - Prob. 116SECh. 10 - Prob. 117SECh. 10 - Prob. 118SECh. 10 - Prob. 119SECh. 10 - Prob. 120SECh. 10 - Prob. 121SECh. 10 - Prob. 122SECh. 10 - A pharmaceutical manufacturer purchases a...Ch. 10 - Prob. 124SECh. 10 - Prob. 125SECh. 10 - Prob. 126SECh. 10 - Prob. 127SECh. 10 - Prob. 128SECh. 10 - Prob. 129SECh. 10 - Prob. 130SE
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
- For a one tailed test evaluating a treatment that is supposed to decrease scores, a researcher obtains t(8) = 1.90. For α = .05, the correct decision is to reject the null hypothesis. true or falsearrow_forwardIf the hypothesis test results in a p-value of 0.08, would we be able to reject the null hypothesis if we were using alpha=0.05? If the hypothesis test results in a p-value of 0.95, would we be able to reject the null hypothesis if we were using alpha=0.05? If the hypothesis test results in a p-value of 0.02, would we be able to reject the null hypothesis if we were using alpha=0.01?arrow_forwardIf the p value is > alpha , what does this mean ? - it proves the Ho is true , with beta error possible - it proves the Ha is true , with alpha error possible - there is sufficient evidence to conclude Ha May be true , with alpha error possible - there is sufficient evidence to conclude that Ho May be true , with beta error possiblearrow_forward
- A new insecticide is advertised to kill more than 95% roaches upon contact. In a laboratory test, the insecticide was applied to 400 roaches and 384 died immediately after contact. Is this sufficient evidence to support the advertised claim? Use α=0.05. (a) Alternative hypothesis for the problem above isarrow_forwardThe shop floor manager in a dairy company believes that the milk packaging process unit for 1 liter packs is not working fine and needs calibration. If the Null Hypothesis is framed to be µ = 1 liter, what would be the alternate hypothesis?arrow_forwardYou complete a hypothesis test using alpha = .05 and based on the evidence from the sample, your decision is to fail to reject the null hypothesis. If the treatment actually does have an effect, which of the following is true?arrow_forward
- An automobile manufacturer claims that the average gas mileage of a new model is 35 miles per gallon (mpg). A consumer group is skeptical of this claim and thinks the manufacturer may be overstating the average gas mileage. If µ represents the true average gas mileage for this new model, which of the following gives the null and alternative hypotheses that the consumer group should test?arrow_forwardA hypothesis test produces a t statistic of t = +2.19. If the researcher is conducting a two-tailed hypothesis test with α = .05, how large does the sample have to be in order to reject the null hypothesis?arrow_forwardA researcher first decided to conduct a two-tailed hypothesis test, with alpha = .05, but then decided she wants to reduce the risk of a Type I error. What should she do? a. Calculate her statistics more carefully. b. Decrease alpha to .01 c. Increase alpha to .15 e. Conduct a three-tailed testarrow_forward
- The designer of a new sheet metal stamping machine claims that their new machine can turn out a certain product faster than the machine now in use. Nine independent trials of stamping the same item on each machine gave the following results on times to completion:. Standard Machine: n1 = 9, x̄1 = 35.22 seconds, s1² = 24.4375 seconds² New Machine: n2 = 9, x̄2 = 31.56 seconds, s2² = 20.0275 seconds² Given the aforementioned data, the hypotheses H0: µ1 - µ2 ≤ 0 and H1: µ1 - µ2 > 0, α = 0.05, and assuming that the both machines have the same variance, is there evidence to substantiate the designer’s claim? a. The t test statistic equals 1.65, so there is sufficient evidence to substantiate the designer’s claim. b. The z test statistic equals 1.75, so there is insufficient evidence to substantiate the designer’s claim. c. The t test statistic equals 1.75, so there is sufficient evidence to substantiate the designer’s claim. d. The t test statistic…arrow_forwardThe designer of a new sheet metal stamping machine claims that their new machine can turn out a certain product faster than the machine now in use. Nine independent trials of stamping the same item on each machine gave the following results on times to completion:. Standard Machine: n1 = 9, x̄1 = 35.22 seconds, s1² = 24.4375 seconds² New Machine: n2 = 9, x̄2 = 31.56 seconds, s2² = 20.0275 seconds² Given the aforementioned data, the hypotheses H0: σ1² ≤ σ2² and H1: σ1² > σ2², and α = 0.05, is there evidence to conclude that σ1² ≤ σ2²? a. The test statistic equals 1.10, so there is evidence to conclude that σ1² ≤ σ2². b. The test statistic equals 0.91, so there is evidence to conclude that σ1² ≤ σ2². c. The test statistic equals 0.91, so there is not evidence to conclude that σ1² ≤ σ2². d. The test statistic equals 1.10, so there is not evidence to conclude that σ1² ≤ σ2². e. The test statistic equals 0.82, so there is not evidence to…arrow_forwardA test of the hypotheses H0: = 7.5 versus Ha: < 7.5 has a probability of making a Type II error of 0.15. What is the power of this test?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 Inc
Probability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage Learning
Statistics 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:PEARSON
The Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. Freeman
Introduction 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