Please make sure your final answers are correct, thanks! Mist (airborne droplets
ID: 3239227 • Letter: P
Question
Please make sure your final answers are correct, thanks!
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):
(a) The investigators performed a simple linear regression analysis to relate the two variables. Does a scatter plot of the data support this strategy?
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.
(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.)
,
mg/m3
x 86 177 192 354 367 442 962 y 0.42 0.60 0.45 0.66 0.63 0.69 0.90 k -XX"x-)x-**)#7 EI *Explanation / Answer
0.000742
r sq=0.874=
87.4% variation in mist can be attributed to the simple linear regression relationship between velocity and mist
solUTIONC:
H0: 1 = 0.0006667
Ha: 1 0.000666
t=5.88
p=0.002
REJECT HO as p<0.05
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.
solutiond:
lower limit=
0.000291
Regression Statistics Multiple R 0.934823 R Square 0.873894 Adjusted R Square 0.848672 Standard Error 0.06238 Observations 7 ANOVA df SS MS F Significance F Regression 1 0.134829 0.134829 34.64909 0.002011 Residual 5 0.019456 0.003891 Total 6 0.154286 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 0.431076 0.040021 10.77138 0.00012 0.3282 0.533952 X 0.000516 8.77E-05 5.886348 0.002011 0.0002910.000742