Homework Help is Here – Start Your Trial Now!
Math
Statistics
Mist (airborne droplets or aerosols) is generated when metal-removing fluids are used in machining operations to cool and lubricate the tool and workpiece. Mist generation is a concern to OSHA, which has recently lowered substantially the workplace standard. An article gave the accompanying data on x = fluid-flow velocity for a 5% soluble oll (cm/sec) and y = the extent of mist droplets having diameters smaller than 10 um (mg/m): 85 177 190 354 360 442 960 y 0.39 0.60 0.45 0.66 0.60 0.69 0.90 (a) The investigators performed a simple linear regression analysis to relate the two variables. Does a scatter plot of the data support this strategy? O Yes, a scatter plot shows a reasonable linear relationship. O No, a scatter plot does not show a reasonable linear relationship. (b) What proportion of observed variation in mist can be attributed to the simple linear regression relationship between velocity and mist? (Round your answer to three decimal places.) (c) The investigators were particularly interested in the impact on mist of increasing velocity from 100 to 1000 (a factor of 10 corresponding to the difference between the smallest and largest x values in the sample). When x increases in this way, is there substantial evidence that the true average increase in y is less than 0.6? (Use a = 0.05.) State the appropriate null and alternative hypotheses. O Ho: B, = 0.0006667 H:B, < 0.0006667 O Ho: B, + 0.0006667 H: B, - 0.0006667 O Ho: B, = 0.0006667 H: B, * 0.0006667 O Ho: B, - 0.0006667 H: B, > 0.0006667 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) P-value = State the conclusion in the problem context. O Fail to reject Ho. There is sufficient evidence that with an increase from 100 to 1000, the true average increase in y is less than 0.6. O Fail to reject Ho. There is not sufficient evidence that with an increase from 100 to 1000, the true average increase in y is less than 0.6. O Reject H. There is sufficient evidence that with an increase from 100 to 1000, the true average Increase in y is less than 0.6. O Reject Ho. There is not sufficient evidence that with an increase from 100 to 1000, the true average increase in y is less than 0.6.

Mist (airborne droplets or aerosols) is generated when metal-removing fluids are used in machining operations to cool and lubricate the tool and workpiece. Mist generation is a concern to OSHA, which has recently lowered substantially the workplace standard. An article gave the accompanying data on x = fluid-flow velocity for a 5% soluble oll (cm/sec) and y = the extent of mist droplets having diameters smaller than 10 um (mg/m): 85 177 190 354 360 442 960 y 0.39 0.60 0.45 0.66 0.60 0.69 0.90 (a) The investigators performed a simple linear regression analysis to relate the two variables. Does a scatter plot of the data support this strategy? O Yes, a scatter plot shows a reasonable linear relationship. O No, a scatter plot does not show a reasonable linear relationship. (b) What proportion of observed variation in mist can be attributed to the simple linear regression relationship between velocity and mist? (Round your answer to three decimal places.) (c) The investigators were particularly interested in the impact on mist of increasing velocity from 100 to 1000 (a factor of 10 corresponding to the difference between the smallest and largest x values in the sample). When x increases in this way, is there substantial evidence that the true average increase in y is less than 0.6? (Use a = 0.05.) State the appropriate null and alternative hypotheses. O Ho: B, = 0.0006667 H:B, < 0.0006667 O Ho: B, + 0.0006667 H: B, - 0.0006667 O Ho: B, = 0.0006667 H: B, * 0.0006667 O Ho: B, - 0.0006667 H: B, > 0.0006667 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) P-value = State the conclusion in the problem context. O Fail to reject Ho. There is sufficient evidence that with an increase from 100 to 1000, the true average increase in y is less than 0.6. O Fail to reject Ho. There is not sufficient evidence that with an increase from 100 to 1000, the true average increase in y is less than 0.6. O Reject H. There is sufficient evidence that with an increase from 100 to 1000, the true average Increase in y is less than 0.6. O Reject Ho. There is not sufficient evidence that with an increase from 100 to 1000, the true average increase in y is less than 0.6.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
Mist (airborne droplets or aerosols) is generated when metal-removing fluids are used in machining operations to cool and lubricate the tool and workpiece. Mist generation is a concern to OSHA, which has recently lowered substantially the workplace standard. An article gave the accompanying data on x = fluid-flow velocity for a 5% soluble oil (cm/sec) and y the extent of mist droplets having diameters smaller than 10 µm (mg/m³): 85 177 190 354 360 442 960 0.39 0.60 0.45 0.66 0.60 0.69 0.90 (a) The investigators performed a simple linear regression analysis to relate the two variables. Does a scatter plot of the data support this strategy? Yes, a scatter plot shows a reasonable linear relationship. No, a scatter plot does not show a reasonable linear relationship. (b) What proportion of observed variation in mist can be attributed to the simple linear regression relationship between velocity and mist? (Round your answer to three decimal places.) (c) The investigators were particularly interested in the impact on mist of increasing velocity from 100 to 1000 (a factor of 10 corresponding to the difference between the smallest and largest x values in the sample). When x increases in this way, is there substantial evidence that the true average increase in y is less than 0.6? (Use a = 0.05.) State the appropriate null and alternative hypotheses. O Ho: B1 = 0.0006667 H: B, < 0.0006667 1 О Но: В, # 0.0006667 Hai B1 0.0006667 HoiB1 = 0.0006667 H: B, + 0.0006667 O Ho: B1 0.0006667 H: B, > 0.0006667 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t = P-value = State the conclusion in the problem context. O Fail to reject Ho. There is sufficient evidence that with an increase from 100 to 1000, the true average increase in y is less than 0.6. Fail to reject Ho. There is not sufficient evidence that with an increase from 100 to 1000, the true average increase in y is less than 0.6. Reject Ho. There is sufficient evidence that with an increase from 100 to 1000, the true average increase in y is less than 0.6. Reject Ho. There is not sufficient evidence that with an increase from 100 to 1000, the true average increase in y is less than 0.6. (d) Estimate the true average change in mist associated with a 1 cm/sec increase in velocity, and do so in a way that conveys information about precision and reliability. (Calculate a 95% CI. Round your answers to sİx decimal places.) mg/m3
Transcribed Image Text:Mist (airborne droplets or aerosols) is generated when metal-removing fluids are used in machining operations to cool and lubricate the tool and workpiece. Mist generation is a concern to OSHA, which has recently lowered substantially the workplace standard. An article gave the accompanying data on x = fluid-flow velocity for a 5% soluble oil (cm/sec) and y the extent of mist droplets having diameters smaller than 10 µm (mg/m³): 85 177 190 354 360 442 960 0.39 0.60 0.45 0.66 0.60 0.69 0.90 (a) The investigators performed a simple linear regression analysis to relate the two variables. Does a scatter plot of the data support this strategy? Yes, a scatter plot shows a reasonable linear relationship. No, a scatter plot does not show a reasonable linear relationship. (b) What proportion of observed variation in mist can be attributed to the simple linear regression relationship between velocity and mist? (Round your answer to three decimal places.) (c) The investigators were particularly interested in the impact on mist of increasing velocity from 100 to 1000 (a factor of 10 corresponding to the difference between the smallest and largest x values in the sample). When x increases in this way, is there substantial evidence that the true average increase in y is less than 0.6? (Use a = 0.05.) State the appropriate null and alternative hypotheses. O Ho: B1 = 0.0006667 H: B, < 0.0006667 1 О Но: В, # 0.0006667 Hai B1 0.0006667 HoiB1 = 0.0006667 H: B, + 0.0006667 O Ho: B1 0.0006667 H: B, > 0.0006667 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t = P-value = State the conclusion in the problem context. O Fail to reject Ho. There is sufficient evidence that with an increase from 100 to 1000, the true average increase in y is less than 0.6. Fail to reject Ho. There is not sufficient evidence that with an increase from 100 to 1000, the true average increase in y is less than 0.6. Reject Ho. There is sufficient evidence that with an increase from 100 to 1000, the true average increase in y is less than 0.6. Reject Ho. There is not sufficient evidence that with an increase from 100 to 1000, the true average increase in y is less than 0.6. (d) Estimate the true average change in mist associated with a 1 cm/sec increase in velocity, and do so in a way that conveys information about precision and reliability. (Calculate a 95% CI. Round your answers to sİx decimal places.) mg/m3
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
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 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…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
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
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS