TEMP PROPPASS -262 0.315 -265 0.202 -256 0.204 -267 0.62 -270 0.715 -272 0.935 -

Question

TEMP PROPPASS -262 0.315 -265 0.202 -256 0.204 -267 0.62 -270 0.715 -272 0.935 -272.4 0.957 -272.7 0.906 -272.8 0.985 -272.9 0.987 3. Quantum Tunneling. At temperatures approaching absolute zero (-273 Celsius helium exhibits traits that defy many laws of conventional physics. An experiment has been conducted with helium in solid form at various temperatures near absolute zero. The solid helium is placed in a dilution refrigerator along with a solid impure substance and the proportion of the impurity passing through the solid helium is recorded. This phenomenon, of solids passing directly through solids, is known as quantum tunnel- ing. The spreadsheet "HELIUM contains the data from this experiment. (a Find the least-squares regression line and plot it on the graph, along with the data points. Use temperature as the independent variable (i.e., the r-value) Also, report the estimated Bo, B1, and o2 values (b) Create a plot of the residuals, and create a normal scores plot. Comment on whether or not you think the linear regression assumptions are satisfied. (c) Via a test on BI, test the hypothesis that the temperature contributes no in formation to the prediction of the proportion of the impurity passing through helium. (d) Construct a 90% confidence interval for Bi (e) Find the coefficient of determination for your model and interpret its value. (f) Construct a 99% prediction interval for the proportion of impurity passing through helium when the temperature is -270 C. g) Estimate the mean proportion of impurity passing through helium at -270 C using a 99% confidence interval.

Explanation / Answer

Please find minitab output you will get the answers in bold.

Regression Analysis: PROPPASS versus TEMP

Analysis of Variance

Source      DF Adj SS   Adj MS F-Value P-Value
Regression   1 0.8309 0.83089    46.73    0.000
TEMP       1 0.8309 0.83089    46.73    0.000
Error        8 0.1423 0.01778
Total        9 0.9731

Model Summary

       S    R-sq R-sq(adj) R-sq(pred)
0.133347 85.38%     83.56%      65.04%

Coefficients

Term          Coef SE Coef T-Value P-Value   VIF
Constant    -13.49     2.07    -6.51    0.000
TEMP      -0.05283 0.00773    -6.84    0.000 1.00

Regression Equation

PROPPASS = -13.49 - 0.05283 TEMP

Fits and Diagnostics for Unusual Observations

Obs PROPPASS     Fit    Resid Std Resid
2    0.2020 0.5093 -0.3073      -2.48 R
3    0.2040 0.0339   0.1701       2.03 R X

R Large residual
X Unusual X

Prediction for PROPPASS

Regression Equation

PROPPASS = -13.49 - 0.05283 TEMP

Prediction for PROPPASS

Regression Equation

PROPPASS = -13.49 - 0.05283 TEMP

Variable Setting
TEMP         -270

     Fit     SE Fit         99% CI                99% PI
0.773466 0.0442136 (0.625112, 0.921820) (0.302081, 1.24485)

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