At temperatures approaching absolute zero ( ), helium

Chapter 11, Problem 95SE

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At temperatures approaching absolute zero (−273◦C), 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.

a Fit a least-squares line to the data.

b Test the null hypothesis \(H_{0}: \beta_{1}=0\) against the alternative hypothesis \(H_{a}: \beta_{1}<0\), at the \(\alpha=.01) level of significance.

c Find a 95% prediction interval for the percentage of the solid impurity passing through solid helium at −273◦C. (This value of x is outside the experimental region where use of the model for prediction may be dangerous.)

Equation transcription:

Text transcription:

H{0}: beta{1}=0

H{a}: beta{1}<0

alpha=.01

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