Mist (airborne droplets or aerosols) is generated when metal-removing fluids are used in machining operations to com 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) a y the extent of mist droplets having diameters smaller than 10 µm (mg/m³): 367 442 962 *19 y 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 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. 90 177 185 354 (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 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: P₁ 0.0006667 H₂: P₁ < 0.0006667 O Ho: P1" Ha: ₁ 0.0006667 0.0006667 = 0.0006667 O Ho: P1" H: ₁ 0.0006667 0.0006EET
Mist (airborne droplets or aerosols) is generated when metal-removing fluids are used in machining operations to com 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) a y the extent of mist droplets having diameters smaller than 10 µm (mg/m³): 367 442 962 *19 y 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 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. 90 177 185 354 (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 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: P₁ 0.0006667 H₂: P₁ < 0.0006667 O Ho: P1" Ha: ₁ 0.0006667 0.0006667 = 0.0006667 O Ho: P1" H: ₁ 0.0006667 0.0006EET
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 21PFA
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