Mist (airborne droplets or aerosols) is generated when metal-removing fluids are used in machining operations to cool andlubricate the tool and workpiece. Mist generation is a concern to OSHA, which has recently lowered substantially theworkplace standard. An article gave the accompanying data on x = fluid-flow velocity for a 5% soluble oil (cm/sec) andy = the extent of mist droplets having diameters smaller than 10 μm (mg/m³):X 90 177 185 354 367 442 962y 0.44 0.60 0.47 0.66 0.59 0.69 0.98(a) The investigators performed a simple linear regression analysis to relate the two variables. Does a scatter plotof 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 relationshipbetween 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 (afactor of 10 corresponding to the difference between the smallest and largest x values in the sample). When xincreases in this way, is there substantial evidence that the true average increase in y is less than 0.6? (Usea = 0.05.)State the appropriate null and alternative hypotheses.O Ho: ₁ = 0.0006667H₂: B₁- 0.0006667O Ho: P₁ 0.0006667H₂: P₁= 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.Reject Ho. There is not sufficient evidence that with an increase from 100 to 1000, the true averageincrease in y is less than 0.6.O Reject Ho. There is sufficient evidence that with an increase from 100 to 1000, the true average increasein 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 averageincrease in y is less than 0.6.O Fail to reject Ho. There is sufficient evidence that with an increase from 100 to 1000, the true averageincrease 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 waythat conveys information about precision and reliability. (Calculate a 95% CI. Round your answers to six decimalplaces.)mg/m³

Question

Mist (airborne droplets or aerosols) is generated when metal-removing fluids are used in machining operations to cool andlubricate the tool and workpiece. Mist generation is a concern to OSHA, which has recently lowered substantially theworkplace standard. An article gave the accompanying data on x = fluid-flow velocity for a 5% soluble oil (cm/sec) andy = the extent of mist droplets having diameters smaller than 10 μm (mg/m³):X 90 177 185 354 367 442 962y 0.44 0.60 0.47 0.66 0.59 0.69 0.98(a) The investigators performed a simple linear regression analysis to relate the two variables. Does a scatter plotof 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 relationshipbetween 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 (afactor of 10 corresponding to the difference between the smallest and largest x values in the sample). When xincreases in this way, is there substantial evidence that the true average increase in y is less than 0.6? (Usea = 0.05.)State the appropriate null and alternative hypotheses.O Ho: ₁ = 0.0006667H₂: B₁- < 0.0006667O Ho: P₁== 0.0006667H: ₁0.0006667O Ho: P1= 0.0006667H:₁> 0.0006667O Ho: P₁ 0.0006667H₂: P₁= 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.Reject Ho. There is not sufficient evidence that with an increase from 100 to 1000, the true averageincrease in y is less than 0.6.O Reject Ho. There is sufficient evidence that with an increase from 100 to 1000, the true average increasein 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 averageincrease in y is less than 0.6.O Fail to reject Ho. There is sufficient evidence that with an increase from 100 to 1000, the true averageincrease 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 waythat conveys information about precision and reliability. (Calculate a 95% CI. Round your answers to six decimalplaces.)mg/m³

Accepted Answer

Given data:

x
y

90
0.44

177
0.6

185
0.47

354
0.66

367
0.59

442
0.69

962
0.98