Question

I don't need part C. but ONLY PART B, and the Test Statistic and P value written at the bottom.

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 μrn (mg/m 3): x86 177 183 354 361 442 969 y| 0.43 0.60 0.47 0.66 0.61 0.69 0.94 (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? (Round your answer to three decimal places.) 91.233 (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 the sample), when x increases in this way, is there substantial evidence that the true average increase in y is less than 0.67 (use α-0.05.) State the approprlate null and alternatlive hypotheses. values in O Ho: β1-0.0006667 Ha: B1 0.0006667 H0: β1-0.0006667 Ha: β1 > 0.0006667 Ho: ß1-0.0006667 Ha: β1 < 0.0006667 Ho: B1 0.0006667 Ha: β1-0.0006661 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.)

Answer 1

EXCEL Mega Stat) output: Regression Analysis 0.919 r 0.959 Std. Error 0.052 Dep. Var.y ANOVA table Source df 1 0.15398561 5 0.00270002 MS value Regression 0.15398561 Residual 0.01350010 Total 0.16748571 ta 0 013401070057 03 009 confidence interval Regression out variables coefficients std. error 0.0330 0.0005 0.00007226 t (df-5) 12.963 7.552 95% lower 95% upper.std.coeff 0.000 0.959 p-value 4.87E-05 0.4281 0.5130 0.0007 0.34320 Intercept 0006 00004 The proportion of observed variation in mist can be attributed to the simple linear regression relationship between velocity and mist is 0.919

t 7.55 P-value 0.001 Reject Ho There is sufficient evidence that with an increase from 100 to 1000, the true average increase in y is less than 0.6.