An Introduction to Mathematical Statistics and Its Applications (6th Edition)
6th Edition
ISBN: 9780134114217
Author: Richard J. Larsen, Morris L. Marx
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 14.5, Problem 3Q
To determine
The differences from method to method are statistically significant, let
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Two methods of determining fat content in milk are being tested. Samples are taken from 6 different milk cartons and both methods are used on a sample from each container. The readings are
Carton 1 2 3 4 5 6
Method A: 2.2 1.7 2.0 1.9 2.1 2.3
Method B: 1.8 2.1 1.9 1.4 2.1 1.7
(A-B) 4 -4.1 50 .6
From Minitab Output:
N
Method A
Method B
6
6
Mean
2.033
1.833
StDev
.216
.266
Difference
6
.200
.374
To test the null hypothesis Ho that there is no difference in the two methods of determining fat content, the lowest level of significance to reject the null hypothesis is:
OA: 0.20
B: 0.15
OC: 0.25
OD: 0.10
E: 0.05
Exposure to microbial products, especially endotoxin, may have an impact on vulnerability to allergic diseases. The following are data on concentration (EU/mg) in settled dust for one sample of urban homes and another of farm homes.
U: 6.0 5.0 11.0 33.0 4.0 5.0 80.0 18.0 35.0 17.0 23.0
F: 6.0 13.0 13.0 8.0 9.0 6.0
2.0 17.0
6.0 8.2 21.0 9.7 3.0 2.0 0.5
n USE SALT
(a) Determine the sample mean for each sample. (Round your answers to four decimal places.)
urban homes
EU/mg
farm homes
EU/mg
How do they compare?
O The average endotoxin concentration in urban homes is more than double the average concentration in farm homes.
O The average endotoxin concentration in farm homes is more than double the average concentration in urban homes.
O The average endotoxin concentration is about the same in both urban and farm homes.
(b) Determine the sample median for each sample.
urban homes
EU/mg
farm homes
EU/mg
How do they compare?
O The median endotoxin concentration is about the same in both urban…
In a study conducted in Italy, 10 patients with hypertriglyceridemia were placed on a low-fat, high-carbohydrate diet. Before the start of the diet, cholesterol and triglyceride measurements were recorded for each subject. Patient Cholesterol Level (mmol/l) Triglyceride level (mmol/l) 1 5.12 2.30 2 6.18 2.54 3 6.77 2.95 4 6.65 3.77 5 6.36 4.18 6 5.90 5.31 7 5.48 5.53 8 6.02 8.83 9 10.34 9.48 10 8.51 14.20A. Use STATA to Calculate the Spearman rank correlation coefficient, rs, for these data. B. Using rs, test the null hypothesis that the population correlation, ρ, equals 0.
Chapter 14 Solutions
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
Ch. 14.2 - Recall the data in Question 8.2.9 giving the sizes...Ch. 14.2 - Test H0==0.12 versus H1=0.12 for the release chirp...Ch. 14.2 - Below are n=50 computer-generated observations...Ch. 14.2 - Let Y1,Y2,...,Y22 be a random sample of normally...Ch. 14.2 - Suppose that n=7 paired observations, (Xi,Yi), are...Ch. 14.2 - Analyze the Shoshoni rectangle data (Case Study...Ch. 14.2 - Recall the FEV1/VC data described in Question...Ch. 14.2 - Do a sign test on the ESP data in Question 13.2.2....Ch. 14.2 - In a marketing research test, twenty-eight adult...Ch. 14.2 - Suppose that a random sample of size...
Ch. 14.2 - Prob. 11QCh. 14.3 - The average energy expenditures for eight elderly...Ch. 14.3 - Prob. 2QCh. 14.3 - Prob. 3QCh. 14.3 - Prob. 4QCh. 14.3 - Prob. 5QCh. 14.3 - DoaWilcoxon signed rank test on the hemoglobin...Ch. 14.3 - Prob. 7QCh. 14.3 - Prob. 8QCh. 14.3 - Prob. 9QCh. 14.3 - Prob. 10QCh. 14.4 - Prob. 1QCh. 14.4 - Prob. 2QCh. 14.4 - Prob. 3QCh. 14.4 - Prob. 4QCh. 14.4 - Prob. 5QCh. 14.4 - A sample of ten 40-W light bulbs was taken from...Ch. 14.4 - Prob. 7QCh. 14.4 - Prob. 8QCh. 14.5 - The following data come from a field trial set up...Ch. 14.5 - Prob. 2QCh. 14.5 - Prob. 3QCh. 14.5 - Prob. 4QCh. 14.5 - Prob. 5QCh. 14.5 - Prob. 6QCh. 14.6 - Prob. 1QCh. 14.6 - Listed below for two consecutive fiscal years are...Ch. 14.6 - Prob. 3QCh. 14.6 - Prob. 4QCh. 14.6 - Prob. 5QCh. 14.6 - Prob. 6Q
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
- In a study conducted in Italy, 10 patients with hypertriglyceridemia were placed on a low-fat, high-carbohydrate diet. Before the start of the diet, cholesterol and triglyceride measurements were recorded for each subject. Patient Cholesterol Level (mmol/l) Triglyceride level (mmol/l) 1 5.12 2.30 2 6.18 2.54 3 6.77 2.95 4 6.65 3.77 5 6.36 4.18 6 5.90 5.31 7 5.48 5.53 8 6.02 8.83 9 10.34 9.48 10 8.51 14.20 a. Construct a two-way scatter plot for these data. b. Use STATA to calculate Pearson’s Correlation Coefficient for these data. c. Test, α = 0.05, whether or not the population correlation, ρ, equals 0.arrow_forwardThe respiratory disturbance index (RDI), which is the number of apneic and hypopneic episodes per hour of sleep, was used as a measure of severity of sleep apnea. An RDI of 5 or more indicates sleep-related breathing disturbances. The RDIs for the females and males samples in a study in US are as follows. Female 0.1 0.5 0.3 2.3 2.0 1.4 0.0 Male 2.6 19.3 1.4 1.0 0.0 39.2 4.1 0.0 2.1 1.1 5.6 5.0 7.0 2.3 4.3 7.5 16.5 7.8 3.3 8.9 7.3 At the 1% significance level, do the data provide sufficient evidence to conclude that the female patients are less suffer than male from the apnea disease?arrow_forwardSamples were collected from two ponds in the Bahamas to compare salinity values (in parts per thousand). Several samples were drawn at each site. Pond 1: 37.03, 37.45, 36.75, 37.54, 37.71, 37.02, 37.32 Pond 2: 38.89, 39.05, 38.51, 38.53, 38.71 Use a 2% significance level to test the claim that the two ponds have the same mean salinity value. Assume that nothing is known about the population distribution of salinities. (a) Enter the rank values in the same order as in the original sample. The rank values for Pond 1 are: The rank values for Pond 2 are: (b) The test statistic is: . (c) The test critical value is: . (d) The conclusion isA. There is not sufficient evidence to indicate that the two ponds have different distributions of salinity values.B. There is sufficient evidence to indicate that the two ponds have different distributions of salinity values.arrow_forward
- Samples of both surface soil and subsoil were taken from eight randomly selected agricultural locations in a particular county. The soil samples were analyzed to determine both surface pH and subsoil pH, with the results shown in the accompanying table. 2. 3. 6. Location Surface pH 6.55 5.98 5.59 6.17 5.92 6.18 6.43 5.68 Subsoil pH 6.78 6.14 5.80 5.91 6.10 6.01 6.18 5.88 a. Compute a 90% confidence interval for the mean differend between surface and subsoil pH for agricultural land in this county. b. What assumptions are necessary for the interval in Part (a) to be valid?arrow_forwardSix bottles of wine of the same variety were analyzed for residual sugar content with the following results: Bottle Percent (w/v) Residual Sugar 1.02, 0.84, 0.99, 1 1.13, 1.02, 1.17, 1.02 3 1.12, 1.32, 1.13, 1.20, 1.25 4 0.77, 0.58, o.61, 0.72 5 0.73, 0.92, 0.90 0.73, 0.88, o.72, 0.70 Evaluate the standard deviation s for each set of data. b. Pool the data to obtain an absolute standard deviation for the method. а.arrow_forwardA certain virus affects 0.7% of the population. A test used to detect the virus in a person is positive 87% of the time if the person has the virus (true positive) and 14% of the time if the person does not have the virus (false positive). Fill out the remainder of the following table and use it to answer the two questions below based on a total sample of 100,000 people. Virus No Virus TotalPositive Test Negative Test Total 100,000a) Find the probability that a person has the virus given that they have tested positive. Round your answer to the nearest hundredth of a percent and do not include a percent sign. % b) Find the probability that a person does not have the virus given that they test negative. Round your answer to the nearest hundredth of a percent and do not include a percent sign. %arrow_forward
- A manufacturing company glues one part to another part during the assembly of its final product. Either too much or too little glue presents a problem. It is important for the pressure of the glue nozzle (pounds per square inch) to be set correctly because it affects the amount of glue (ounces) that is applied. Ten applications are sampled and the following information collected: SSXX = 129.6 SSYY = 2.345 SSXY = 16.6 X bar = 25.2 Y bar = 2.05 Interpret the coefficient of determinationarrow_forwardThe percentage crude protein content of hay was determined based on 10 bale samples collected from each of four locations (plots as treatments) on a large ranch as follows: Plot A 12.8 13.4 11.2 11.6 9.4 10.3 14.1 11.9 10.5 10.4 b. Plot B 8.1 10.3 4.2 7.8 5.6 8.1 12.7 6.8 6.9 6.4 Plot C 9.8 10.6 9.1 4.3 11.2 11.6 8.3 8.9 9.2 6.4 Plot D 16.4 8.2 15.1 10.4 7.8 9.2 12.6 11.0 8.0 9.8 Set up and complete an ANOVA table for a one-way analysis. Show all work.arrow_forwardIn an existing process, we have found that the lower and upper control limits for X-bar chart are 8.09 and 8.59 respectively. Whereas, the lower and upper control limits for R-chart are 0 to 1.25 respectively. The following measurements for one sample are taken: 8.5, 9.14, 8.28, and 9.2. Using both the X-bar chart and R-chart for this particular sample, what we can conclude about the overall process a. Insufficient information to conclude Ob. Process is in-control O c. Perfect process O d. Process is out-of-control.arrow_forward
- A cigarette manufacturer claims that his cigarettes have nicotine content that does not exceed 2.0 milligrams. If a random sample of 10 cigarettes of this type have nicotine contents of 2.0, 2.3 1.7, 2.2, 1.9, 2.2, 2.0, 2.5, 2.1 and 1.9 milligrams, would you agree with the manufacturer's claim? a = 0.05 what is the correct set of hypotheses to test this claim? A HO:µ 2.0 D) H0:μ= 2.0; H1: μ + 2.0arrow_forwardFluoride Exposure in Drinking Water Exercise 2.250 introduces a study showing that fluoride exposure might have long-term negative consequences for the offspring of pregnant women. Part of the study examines the effect of adding fluoride to tap water on mean fluoride concentration in women. Summary statistics for fluoride concentration (measured in mg/L) for the two groups are given in the table below. Tap water Fluoridated Non-fluoridated Conclusion: Sample size 141 228 Mean 0.69 0.40 St.Dev. 0.42 0.27 Find and interpret a 99% confidence interval for the mean increase in fluoride concentration for those with fluoridated tap water. Let Group 1 represent those with fluoridated tap water and Group 2 represent those without fluoridated tap water. Confidence interval: i to i (round to three decimal places)arrow_forwardAnalysis of several plant-food preparations for potassium ion yielded the following data: Sample Percent K* 1 6.02, 6.04, 5.88, 6.06, 5.82 2 7.48, 7.47, 7.29 3.90, 3.96, 4.16, 3.96 4 4.48, 4.65, 4.68, 4.42 5 5.29, 5.13, 5.14, 5.28, 5.20 The preparations were randomly drawn from the same population. a) Find the standard deviation s for each sample. b) Obtain the pooled value Spooled- c) Why is spooled a better estimate of s than the standard deviation from any one sample?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