a. Please write down the theoretical model and estimated linear model for this data. b. Test the null hypothesis that the true slope is 0; be sure to include null, alternative hypotheses, test method, and interpret your results. c. Use a 95% confidence interval to estimate the slope ß₁. Does the interval support the hypothesis that temperature is useful to predict the proportion of impurity passing through helium at alpha=0.05? d. Report and interpret the coefficient of determination for this model e. Find a 95% prediction interval for the percentage of impurity passing through solid helium at -272°C.
a. Please write down the theoretical model and estimated linear model for this data. b. Test the null hypothesis that the true slope is 0; be sure to include null, alternative hypotheses, test method, and interpret your results. c. Use a 95% confidence interval to estimate the slope ß₁. Does the interval support the hypothesis that temperature is useful to predict the proportion of impurity passing through helium at alpha=0.05? d. Report and interpret the coefficient of determination for this model e. Find a 95% prediction interval for the percentage of impurity passing through solid helium at -272°C.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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![At temperatures approaching absolute zero (-273°C), helium exhibits traits that
seem to defy many laws of Newtonian 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. (This phenomenon of solid passing directing
through solids is known as quantum tunneling.) Researchers wants to know the relationship
between temperature and proportion of impurity. They use a linear model with proportion of
impurity being the response. The data is in the following:
Temperature, x°C
-262.0
-265.0
-256.0
-267.0
-270.0
-272.0
-272.4
-272.7
-272.8
-272.9
Proportion of impurity, y
.315
.202
.204
.620
.715
.935
.957
.906
.985
.987](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5dfcde0a-cc8e-4f7e-b5e2-9ec6ad36a3c9%2F58d9df13-d392-4052-a07a-ca48d47bf527%2Fir5cpym_processed.png&w=3840&q=75)
Transcribed Image Text:At temperatures approaching absolute zero (-273°C), helium exhibits traits that
seem to defy many laws of Newtonian 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. (This phenomenon of solid passing directing
through solids is known as quantum tunneling.) Researchers wants to know the relationship
between temperature and proportion of impurity. They use a linear model with proportion of
impurity being the response. The data is in the following:
Temperature, x°C
-262.0
-265.0
-256.0
-267.0
-270.0
-272.0
-272.4
-272.7
-272.8
-272.9
Proportion of impurity, y
.315
.202
.204
.620
.715
.935
.957
.906
.985
.987
![a. Please write down the theoretical model and estimated linear model for this data.
b. Test the null hypothesis that the true slope is 0; be sure to include null, alternative hypotheses,
test method, and interpret your results.
c. Use a 95% confidence interval to estimate the slope ß₁. Does the interval support the
hypothesis that temperature is useful to predict the proportion of impurity passing through
helium at alpha=0.05?
d. Report and interpret the coefficient of determination for this model
e. Find a 95% prediction interval for the percentage of impurity passing through solid helium at
-272°C.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5dfcde0a-cc8e-4f7e-b5e2-9ec6ad36a3c9%2F58d9df13-d392-4052-a07a-ca48d47bf527%2Fw076g4r_processed.png&w=3840&q=75)
Transcribed Image Text:a. Please write down the theoretical model and estimated linear model for this data.
b. Test the null hypothesis that the true slope is 0; be sure to include null, alternative hypotheses,
test method, and interpret your results.
c. Use a 95% confidence interval to estimate the slope ß₁. Does the interval support the
hypothesis that temperature is useful to predict the proportion of impurity passing through
helium at alpha=0.05?
d. Report and interpret the coefficient of determination for this model
e. Find a 95% prediction interval for the percentage of impurity passing through solid helium at
-272°C.
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