An Introduction to Statistical Methods and Data Analysis
7th Edition
ISBN: 9781305269477
Author: R. Lyman Ott, Micheal T. Longnecker
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 2.8, Problem 18E
In the descriptions of experiments given in Exercises 2.15–2.18, identify the important features of each design. Include as many of the components listed in Exercise 2.14 as needed to adequately describe the design.
2.18 Researchers in an education department at a large state university have designed a study to compare the math abilities of students in junior high. They will also examine the impact of three types of schools — public, private nonparochial, and parochial — on the scores the students receive in a standardized math test. Two large cities in each of four geographical regions of the United States were selected for the study. In each city, one school of each of the three types was randomly selected, and a single eighth-grade class was randomly selected within each school.
The scores on the test were recorded for each student in the selected classrooms. The researcher was concerned about differences in socio-economie status among the 8 cities, so she obtained a measure of socioeconomic status for each of the students that participated in the study.
2.14 The process engineer designed a study to evaluate the quality of plastic irrigation pipes. The study involved a total of 48 pipes; 24 pipes were randomly selected from each of the company’s two manufacturing plants. The pipes were heat-treated at one one of four temperatures (175, 200, 225, 250°F). The pipes were chemically treated with one of three types of hardeners (H1, H2, H3). The deviations from the nominal compressive strength were measured at five locations on each of the pipes.
Identify each of the following components of the experimental design.
- a. Factors
- b. Factor levels
- c. Blocks
- d. Experimental unit
- e. Measurement unit
- f. Replications
- g.
Covariates - h. Treatments
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A coffee company uses a data-based approach to improving the quality and customer satisfaction of its products. When survey data indicated that the coffee company needed to improve its package-sealing process, an experiment was conducted to determine the factors in the bag-sealing equipment that might be affecting the ease of opening the bag without tearing the inner liner of the bag. One factor that could affect the rating of the ability of the bag to resist tears was the plate gap on the bag-sealing equipment. Data were collected on 19 bags in which the plate gap was varied.
1) Assuming a linear relationship, use the least-squares method to find the regression coefficients b0 and b1.
2) Interpret the meaning of the slope, b1, in this problem. Choose the correct answer below.
A. For each increase of one in the tear rating, the plate gap is expected to increase by b1 units.
B. The approximate tear rating when the plate gap is 0 units is b1.
C. The…
A coffee company uses a data-based approach to improving the quality and customer satisfaction of its products. When survey data indicated that the coffee company needed to improve its package-sealing process, an experiment was conducted to determine the factors in the bag-sealing equipment that might be affecting the ease of opening the bag without tearing the inner liner of the bag. One factor that could affect the rating of the ability of the bag to resist tears was the plate gap on the bag-sealing equipment. Data were collected on 19 bags in which the plate gap was varied.
A) Assuming a linear relationship, use the least-squares method to find the regression coefficients b0 and b1.
Interpret the meaning of the slope, b1,in this problem. Choose the correct answer below.
A.For each increase of one in the tear rating, the plate gap is expected to increase by b1 units.
B. The approximate tear rating when the plate gap is 0 units is b1.
C. The approximate…
This obstetrician also wanted to determine the impact that three experimental diets had on the birth weights of pregnant mothers. She was also interested if age had an impact on birth weights. She randomly selected 27 pregnant mothers in the first trimester of whom 9 were 20 to 29 years old, 9 were 30 to 39 years old, and 9 were 40 or older. For each age group, she randomly assigned the mothers to one of three diets. After delivery, she measured the birth weight (in grams) of the babies and obtained the data
a) What is the blocking variable?
Chapter 2 Solutions
An Introduction to Statistical Methods and Data Analysis
Ch. 2.8 - In the following descriptions of a study,...Ch. 2.8 - In the following descriptions of a study,...Ch. 2.8 - A news report states that minority children who...Ch. 2.8 - A study was conducted to determine if the...Ch. 2.8 - Prob. 5ECh. 2.8 - A large auto parts supplier with distribution...Ch. 2.8 - The circuit judges in a rural county are...Ch. 2.8 - Prob. 8ECh. 2.8 - Time magazine, in an article in the late 1950s,...Ch. 2.8 - The New York City school district is planning a...
Ch. 2.8 - A professional society, with a membership of...Ch. 2.8 - For each of the following situations, decide what...Ch. 2.8 - For each of the following situations, decide what...Ch. 2.8 - The process engineer designed a study to evaluate...Ch. 2.8 - Prob. 15ECh. 2.8 - In the descriptions of experiments given in...Ch. 2.8 - In the descriptions of experiments given in...Ch. 2.8 - In the descriptions of experiments given in...Ch. 2.8 - A research specialist for a large seafood company...Ch. 2.8 - In Exercises 2.20–2.22, identify whether the...Ch. 2.8 - In Exercises 2.202.22, identify whether the design...Ch. 2.8 - In Exercises 2.20–2.22, identify whether the...Ch. 2.8 - A bakery wants to evaluate new recipes for carrot...Ch. 2.8 - Prob. 24SECh. 2.8 - Prob. 25SECh. 2.8 - Prob. 26SECh. 2.8 - Prob. 27SECh. 2.8 - Prob. 28SECh. 2.8 - Prob. 29SECh. 2.8 - A forester wants to estimate the total number of...Ch. 2.8 - A transportation researcher is funded to estimate...Ch. 2.8 - The department of agriculture in a midwestern...Ch. 2.8 - Prob. 33SECh. 2.8 - A Yankelovich, Skelly, and White poll taken in the...
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
- A coffee company uses a data-based approach to improving the quality and customer satisfaction of its products. When survey data indicated that the coffee company needed to improve its package-sealing process, an experiment was conducted to determine the factors in the bag-sealing equipment that might be affecting the ease of opening the bag without tearing the inner liner of the bag. One factor that could affect the rating of the ability of the bag to resist tears was the plate gap on the bag-sealing equipment. Data were collected on 19 bags in which the plate gap was varied. Assuming a linear relationship, use the least-squares method to find the regression coefficients b0 and b1. b0 = b1 =arrow_forwardThis obstetrician also wanted to determine the impact that three experimental diets had on the birth weights of pregnant mothers. She was also interested if age had an impact on birth weights. She randomly selected 27 pregnant mothers in the first trimester of whom 9 were 20 to 29 years old, 9 were 30 to 39 years old, and 9 were 40 or older. For each age group, she randomly assigned the mothers to one of three diets. After delivery, she measured the birth weight (in grams) of the babies and obtained the data a)How many treatments are there? b)What type of design is this? How many replications are there within each cell?arrow_forwardJoan's Nursery specializes in custom-designed landscaping for residential areas. The estimated labor cost associated with a particular landscaping proposal is based on the number of plantings of trees, shrubs, and so on to be used for the project. For cost estimating purposes, managers use two hours of labor time for the planting of a medium-sized tree. Actual times from a sample of 10 plantings during the past month follow (times in hours), 2.7 2.2 2.4 3.3 1.6 1.5 2.4 2.5 1.7 2.8 With a 0.05 level of significance, test to see whether the mean tree-planting time differs from two hours. a. State the null and alternative hypotheses. Ho : 4- Select your answer- V2 H, :- Select your answer - V b. Compute the sample mean. (to 2 decimals) c. Compute the sample standard deviation. (to 4 decimals) d. Find the test statistic and p-value. (Use Table 2 in Appendix B.) (to 3 decimals) p-value -Select your answer e. What is your conclusion? We-Select your answer- Vreject the null hypothesis. There-…arrow_forward
- You may need to use the appropriate technology to answer this question. An automobile dealer conducted a test to determine if the time in minutes needed to complete a minor engine tune-up depends on whether a computerized engine analyzer or an electronic analyzer is used. Because tune-up time varies among compact, intermediate, and full-sized cars, the three types of cars were us blocks in the experiment. The data obtained follow. Analyzer Computerized Electronic Compact 50 41 Car Intermediate 54 44 Full-sized 64 47 Use a = 0.05 to test for any significant differences. State the null and alternative hypotheses. O Ho: MCompact = "Intermediate = "Full-sized H: "Compact *"Intermediate * Full-sized O Ho: "Compact * "Intermediate * Full-sized H: "Compact = "Intermediate "Full-sized O Ho: "Computerized = HElectronic H: "Computerized * "Electronic O Ho: "Computerized = "Electronic = "Compact = 4Intermediate = "Full-sized H: Not all the population means are equal. O Ho: "Computerized *…arrow_forwarda) An experimenter, Mr Mafanela would like to investigate the effects of a treatment with five levels A, B, C, D, and E. However he could only afford to take twenty observations in five blocks which could only be of size four each. (i) Sketch the layout of the data. (ii) Check whether Mr Mafanela design is balanced or not.arrow_forwardAbsenteeism: Absenteeism can be a serious employment problem. It is estimated that absenteeism reduces potential output by more than 10%. Two economists launched a research project to learn more about the problem. They randomly selected 100 organizations to participate in a 1-year study. For each organization, they recorded the average number of days absent per employee and several variables thought to affect absenteeism. Management’s goal here is to analyze the data and determine which factors may be helpful in predicting absenteeism. Now let us build a model to predict absenteeism based on key independent variables available in this dataset; wage, PctPT, PctU, Av Shift and U/MRel. Correlation matrix is provided below. Why are the variables AvShift and U/MRel excluded from this correlation matrix? Which variable in the matrix is likely to provide the best simple linear regression model and why? Does the correlation matrix show any evidence of collinearity? Explain. Data:…arrow_forward
- Absenteeism: Absenteeism can be a serious employment problem. It is estimated that absenteeism reduces potential output by more than 10%. Two economists launched a research project to learn more about the problem. They randomly selected 100 organizations to participate in a 1-year study. For each organization, they recorded the average number of days absent per employee and several variables thought to affect absenteeism. Management’s goal here is to analyze the data and determine which factors may be helpful in predicting absenteeism. Now let us build a model to predict absenteeism based on key independent variables available in this dataset; wage, PctPT, PctU, Av Shift and U/MRel The following down below is the correlation matrix between absenteeism and potential independent variables. Why are the variables AvShift and U/MRel excluded from this correlation matrix? Which variable in the matrix is likely to provide the best simple linear regression model and why? Does the…arrow_forwardAbsenteeism: Absenteeism can be a serious employment problem. It is estimated that absenteeism reduces potential output by more than 10%. Two economists launched a research project to learn more about the problem. They randomly selected 100 organizations to participate in a 1-year study. For each organization, they recorded the average number of days absent per employee and several variables thought to affect absenteeism. Management’s goal here is to analyze the data and determine which factors may be helpful in predicting absenteeism. Perform a two-sample t-test analysis to determine if mean absenteeism is different between organizations which have a good Union management and those that do not. I have provided the F-test for two variances below: Copy and paste the Two sample t-test output below AND provide a clear conclusion supported by key statistics in the output about how absenteeism is affected by the Union Management Relationship. (I just need to know how to perform the two…arrow_forwardRhino viruses typically cause common colds. In a test of the effectiveness of echinacea, 43 of the 50 subjects treated with echinacea developed rhinovirus infections. In a placebo group, 97 of the 111 subjects developed rhinovirus infections. Use a 0.05 significance level to test the claim that echinacea has an effect on rhinovirus infections. Complete parts (a) through (c) below.arrow_forward
- Rhino viruses typically cause common colds. In a test of the effectiveness of echinacea, 41 of the 47 subjects treated with echinacea developed rhinovirus infections. In a placebo group, 74 of the 90 subjects developed rhinovirus infections. Use a 0.01 significance level to test the claim that echinacea has an effect on rhinovirus infections. Complete parts (a) through (c) below. H0: p1=p2 H1: p1≠p2 a. Test the claim using a hypothesis test. Consider the first sample to be the sample of subjects treated with echinacea and the second sample to be the sample of subjects treated with a placebo. What are the null and alternative hypotheses for the hypothesis test? Identify the test statistic. z = _________ Identify the P-value p-value = _________arrow_forwardA study was conducted to assess the influence of various factors on the start of new firms in the computer chip industry. For a sample of 70 countries the following model was estimated: ŷ = -59.31 + 4.983x1 + 2.198x2 + 3.816x3 – 0.310x4 (1.156) (0.210) (2.063) (0.330) -0.886x5 + 3.215x6 + 0.85x7 (3.055) (1.568) (0.354) R2 = 0.766 where ŷ = new business starts in the industry X1 = population in millions X2 = industry size x3 = measure of economic quality of life measure of political quality of life measure of environmental quality of life measure of health and educational quality of life X4 X5 X6 = x7 = measure of social quality of life The numbers in parentheses under the coefficients are the estimated coefficient standard errors. (a) Determine which coefficients in the model are statistically significant? Provide a justification for your answer. (b) Is the overall regression equation statistically significant at the 1% level? Justify your answer.arrow_forwardYou may need to use the appropriate technology to answer this question. An automobile dealer conducted a test to determine if the time in minutes needed to complete a minor engine tune-up depends on whether a computerized engine analyzer or an electronic analyzer is used. Because tune-up time varies among compact, intermediate, and full-sized cars, the three types of cars were used as blocks in the experiment. The data obtained follow. Analyzer computerized electronic Car compact 50 41 Intermediate 56 45 Full Sized 62 46 Use ? = 0.05 to test for any significant differences. State the null and alternative hypotheses. H0: ?Computerized = ?ElectronicHa: ?Computerized ≠ ?ElectronicH0: ?Computerized ≠ ?ElectronicHa: ?Computerized = ?Electronic H0: ?Computerized = ?Electronic = ?Compact = ?Intermediate = ?Full-sizedHa: Not all the population means are equal.H0: ?Compact = ?Intermediate = ?Full-sizedHa: ?Compact ≠ ?Intermediate ≠ ?Full-sizedH0:…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Hypothesis Testing using Confidence Interval Approach; Author: BUM2413 Applied Statistics UMP;https://www.youtube.com/watch?v=Hq1l3e9pLyY;License: Standard YouTube License, CC-BY
Hypothesis Testing - Difference of Two Means - Student's -Distribution & Normal Distribution; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=UcZwyzwWU7o;License: Standard Youtube License