At temperatures approaching absolute zero (273C), helium exhibits traits that defy many

Chapter 11, Problem 11.95

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At temperatures approaching absolute zero (273C), 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 fraction (in weight) of the impurity passing through the solid helium is recorded. (The phenomenon of solids passing directly through solids is known as quantum tunneling.) The data are given in the following table. Proportion of Impurity Passing C Temperature (x) Through Helium (y) 262.0 .315 265.0 .202 256.0 .204 267.0 .620 270.0 .715 272.0 .935 272.4 .957 272.7 .906 272.8 .985 272.9 .987 a Fit a least-squares line to the data. b Test the null hypothesis H0: 1 = 0 against the alternative hypothesis Ha : 1 < 0, at the = .01 level of significance. c Find a 95% prediction interval for the percentage of the solid impurity passing through solid helium at 273C. (This value of x is outside the experimental region where use of the model for prediction may be dangerous.)