Mist (airborne droplets or aerosols) is generated when metal-removing fluids are
ID: 3178567 • Letter: M
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 mu m (mg/m^3): (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? () 0.904 (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 alpha = 0.05.) State the appropriate null and alternative hypotheses. H_0: beta_1 = 0.0006667 H_a: beta_1 notequalto 0.0006667 H_0: beta_1 = 0.0006667 H_a: beta_1 0.0006667 H_0: beta_1 notequalto 0.0006667 H_a: beta_1 = 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.) State the conclusion in the problem context. Fail to reject H_0. 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 H_0. There is sufficient evidence that with an increase from 100 to 1000, the true average increase in y is less than 0.6. Reject H_0. There is not sufficient evidence that with an increase from 100 to 1000, the true average increase in y is less than 0.6. Fail to reject H_0. There is 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.)Explanation / Answer
c) The statistical software output for this test is:
Parameter estimates:
Hence,
t = -1.52
p - value = 0.095
d) The statistical software output for 95% CI is:
Parameter estimates:
Hence,
95% CI is:
(0.000342, 0.000750) mg/m3
Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 0.42748885 0.036241604 0 5 11.795528 <0.0001 Slope 0.00054599614 0.000079423853 < 0.0006667 5 -1.5197431 0.0945