A new thermostat has been engineered for the frozen food cases in large supermarkets. Both the old and new thermostats hold temperatures at an average of 25. However, it is heped that the new thermostat might be more dependable in the sense that it will hold temperatures doser to 25% One frozen food case was equipped with the new thermostat, and a random sample of 21 temperature readings gave a sample variance of 5.1. Another similar frozen food case was equipped with the old thermostat, and a random sample of 15 temperature readings gave a sample variance of 12.4. Test the claim that the population variance of the old thernostat temperature readings is larger than that for the new thermostat. Use a 5% level of significance. How could your test conclusion relate to the question regarding the dependability of the temperature readings? (Let population 1 refer to data from the old tharmostat. (a) What is the level of significance? State the null and altemate hypotheses. (b) Find the value of the sample Fstatistic. (Round your answer to two decimal places.) what are the degrees of freedom? df What assumptions are you making about the original distribution? The populations follow dependent normal distributions. We have random samples from each population. The populations follow independent normal distributions. We have random samples from ach papulation The populations foliow independent chi-squuare distributions We have random samples from each pogulation. The populations folow independent normal distributions fe) ind or estimate the value of the sample tat statistic. (Round your anawer to four decmal places)
A new thermostat has been engineered for the frozen food cases in large supermarkets. Both the old and new thermostats hold temperatures at an average of 25. However, it is heped that the new thermostat might be more dependable in the sense that it will hold temperatures doser to 25% One frozen food case was equipped with the new thermostat, and a random sample of 21 temperature readings gave a sample variance of 5.1. Another similar frozen food case was equipped with the old thermostat, and a random sample of 15 temperature readings gave a sample variance of 12.4. Test the claim that the population variance of the old thernostat temperature readings is larger than that for the new thermostat. Use a 5% level of significance. How could your test conclusion relate to the question regarding the dependability of the temperature readings? (Let population 1 refer to data from the old tharmostat. (a) What is the level of significance? State the null and altemate hypotheses. (b) Find the value of the sample Fstatistic. (Round your answer to two decimal places.) what are the degrees of freedom? df What assumptions are you making about the original distribution? The populations follow dependent normal distributions. We have random samples from each population. The populations follow independent normal distributions. We have random samples from ach papulation The populations foliow independent chi-squuare distributions We have random samples from each pogulation. The populations folow independent normal distributions fe) ind or estimate the value of the sample tat statistic. (Round your anawer to four decmal places)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:### Comparing Thermostat Dependability in Frozen Food Cases
A new thermostat has been engineered for the frozen food cases in large supermarkets. Both the old and new thermostats hold temperatures at an average of 25°F. However, it is hoped that the new thermostat might be more dependable in the sense that it will hold temperatures closer to 25°F. One frozen food case was equipped with the new thermostat, and a random sample of 12 temperature readings gave a sample variance of 5.1. Another similar frozen food case was equipped with the old thermostat, and a random sample of 12 temperature readings gave a sample variance of 12. Test the claim that the population variance of the old thermostat temperature readings is larger than that for the new thermostat, using a 1% level of significance. How could your test conclusion relate to the question regarding the dependability of the temperature readings? (Let population 1 refer to data from the old thermostat.)
### Steps to Conduct the Hypothesis Test:
#### (a) State the level of significance:
1% level of significance (α = 0.01)
#### (b) State the null and alternate hypotheses:
- Null Hypothesis (H₀): \(\sigma_1^2 \leq \sigma_2^2\)
- Alternate Hypothesis (H₁): \(\sigma_1^2 > \sigma_2^2\)
Given choices:
- \(H_0: \sigma_1^2 = \sigma_2^2; H_a: \sigma_1^2 \neq \sigma_2^2\)
- \(H_0: \sigma_1^2 \leq \sigma_2^2; H_a: \sigma_1^2 > \sigma_2^2\) ⬅️
- \(H_0: \sigma_1^2 \geq \sigma_2^2; H_a: \sigma_1^2 < \sigma_2^2\)
#### (c) Find the value of the sample F statistic. (Round your answer to two decimal places.)
Sample F statistic = 2.35
#### (d) Determine the degrees of freedom:
- Degrees of freedom for numerator (\(df_1\)) = 11
- Degrees of freedom for denominator (\(df_2\)) = 11
#### (e) Identify the assumptions being made about the original
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