Need help with (c) and (d) 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): x 88 177 182 354 369 442 970 y 0.39 0.60 0.50 0.66 0.61 0.69 0.92 (a) The investigators performed a simple linear regression analysis to relate the two variables. Does a scatter plot of the data support this strategy? (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 α = 0.05.) State the appropriate null and alternative hypotheses. 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. Reject H0. 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 H0. 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 H0. 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 H0. 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 six decimal places.)

Need help with (c) and (d) 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): x 88 177 182 354 369 442 970 y 0.39 0.60 0.50 0.66 0.61 0.69 0.92 (a) The investigators performed a simple linear regression analysis to relate the two variables. Does a scatter plot of the data support this strategy? (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 α = 0.05.) State the appropriate null and alternative hypotheses. 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. Reject H0. 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 H0. 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 H0. 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 H0. 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 six decimal places.)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 94E

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Need help with (c) and (d)

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):

x	88	177	182	354	369	442	970
y	0.39	0.60	0.50	0.66	0.61	0.69	0.92

(a) The investigators performed a simple linear regression analysis to relate the two variables. Does a scatter plot of the data support this strategy?

(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 α = 0.05.)
State the appropriate null and alternative hypotheses.

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.

Reject H₀. 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 H₀. 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 H₀. 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 H₀. 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 six decimal places.)

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