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 26 temperature readings gave a sample variance of 4.2. Another similar frozen food case was equipped with the old thermostat, and a random sample of 19 temperature readings gave a sample variance of 12.2. Test the claim that the population variance of the old thermostat 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 thermostat.) (a) What is the level of significance? State the null and alternate hypotheses. H0: ?12 = ?22; H1: ?12 ≠ ?22H0: ?12 > ?22; H1: ?12 = ?22    H0: ?12 = ?22; H1: ?12 > ?22H0: ?12 = ?22; H1: ?12 < ?22 (b) Find the value of the sample F statistic. (Round your answer to two decimal places.) What are the degrees of freedom? dfN =  dfD =  What assumptions are you making about the original distribution? The populations follow independent normal distributions. We have random samples from each population.The populations follow independent normal distributions.    The populations follow independent chi-square distributions. We have random samples from each population.The populations follow dependent normal distributions. We have random samples from each population. (c) Find or estimate the P-value of the sample test statistic. (Round your answer to four decimal places.) p-value > 0.1000.050 < p-value < 0.100    0.025 < p-value < 0.0500.010 < p-value < 0.0250.001 < p-value < 0.010p-value < 0.001 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.    At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. (e) Interpret your conclusion in the context of the application. Reject the null hypothesis, there is sufficient evidence that the population variance is larger in the old thermostat temperature readings.Reject the null hypothesis, there is insufficient evidence that the population variance is larger in the old thermostat temperature readings.    Fail to reject the null hypothesis, there is insufficient evidence that the population variance is larger in the old thermostat temperature readings.Fail to reject the null hypothesis, there is sufficient evidence that the population variance is larger in the old thermostat temperature readings.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Topic Video
Question

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 26 temperature readings gave a sample variance of 4.2. Another similar frozen food case was equipped with the old thermostat, and a random sample of 19 temperature readings gave a sample variance of 12.2. Test the claim that the population variance of the old thermostat 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 thermostat.)

(a) What is the level of significance?


State the null and alternate hypotheses.
H0: ?12 = ?22H1: ?12 ≠ ?22H0: ?12 > ?22H1: ?12 = ?22    H0: ?12 = ?22H1: ?12 > ?22H0: ?12 = ?22H1: ?12 < ?22

(b) Find the value of the sample F statistic. (Round your answer to two decimal places.)


What are the degrees of freedom?
dfN
dfD

What assumptions are you making about the original distribution?
The populations follow independent normal distributions. We have random samples from each population.The populations follow independent normal distributions.    The populations follow independent chi-square distributions. We have random samples from each population.The populations follow dependent normal distributions. We have random samples from each population.

(c) Find or estimate the P-value of the sample test statistic. (Round your answer to four decimal places.)
p-value > 0.1000.050 < p-value < 0.100    0.025 < p-value < 0.0500.010 < p-value < 0.0250.001 < p-value < 0.010p-value < 0.001


(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?
At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.    At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.
Reject the null hypothesis, there is sufficient evidence that the population variance is larger in the old thermostat temperature readings.Reject the null hypothesis, there is insufficient evidence that the population variance is larger in the old thermostat temperature readings.    Fail to reject the null hypothesis, there is insufficient evidence that the population variance is larger in the old thermostat temperature readings.Fail to reject the null hypothesis, there is sufficient evidence that the population variance is larger in the old thermostat temperature readings.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 6 steps

Blurred answer
Knowledge Booster
Hypothesis Tests and Confidence Intervals for Means
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman