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 onx= fluid-flowvelocity for a 5% soluble oil (cm/sec) andy= theextent of mist droplets having diameters smaller than 10m (mg/m³)

x 87 177 184 354 367 442 963

y 0.38 0.60 0.48 0.66 0.61 0.69 0.93

a. 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.)

b. 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 largestxvalues in the sample). Whenxincreases in this way, is there substantial evidence that the true average increase inyis less than 0.6? (Use= 0.05.)

State the appropriate null and alternative hypotheses.

Calculate the test statistic and determine theP-value. (Round your test statistic to two decimal places and yourP-value to three decimal places.)

t=

P-value=

c) 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