Heat flow is the passage of thermal energy from a hot to a cold body. This phenomenon is of particular interest to engineers, who attempt to understand and control the flow of heat through the use of thermal insulation and other devices. The data below were taken from heat flow gauge readings for an industrial process over 10 equally spaced time intervals. A concern is that the process may be cooling down as time progresses. One way to check this statistically is to compare the measurements for the first 5 time periods to the measurements for the last 5 time periods.You may assume that heat flow is approximately normal for each group.Time period 1 (Group 1): 9.273, 9.262, 9.243, 9.283, 9.270Time period 2 (Group 2): 9.240, 9.292, 9.284, 9.279, 9.258Unless otherwise stated, give your answers to three decimal places.Construct a 95% confidence interval for the difference in mean heat flow. Give your answers to three decimal places. Use t∗=2.352t∗=2.352.( , ) Conduct a hypothesis test to determine whether the average heat flow is higher in period 1 than period 2. What is the parameter of interest?i. ppii. μμiii. p1−p2p1−p2iv. μ1−μ2μ1−μ2v. μdμd What is the correct null value for this test? What sign should appear in the alternative hypothesis?i. == ii. << iii. >> iv. ≠≠ The test statistic for this test is t=t= . The p-value for this test is . Use df=7.194df=7.194. (If p-value <0.001<0.001, enter 0). Select the appropriate decision for this hypothesis test (use α=0.01α=0.01).i. Reject H0H0 ii. Fail to reject H0H0 iii. Accept H0H0 Select the appropriate interpretation for this hypothesis test (use α=0.01α=0.01).i. We have statistically significant evidence to suggest that the average heat flow is lower in period 2 than 1.ii. We do not have statistically significant evidence to suggest that the average heat flow is lower in period 2 than 1.iii. We have statistically significant evidence to suggest that the average heat flow is the same in period 2 and period 1. If an error had been made on this test, what kind of error would it have been?i. Type I error ii. Type II error

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Answered: Heat flow is the passage of thermal…

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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Heat flow is the passage of thermal energy from a hot to a cold body. This phenomenon is of particular interest to engineers, who attempt to understand and control the flow of heat through the use of thermal insulation and other devices. The data below were taken from heat flow gauge readings for an industrial process over 10 equally spaced time intervals. A concern is that the process may be cooling down as time progresses. One way to check this statistically is to compare the measurements for the first 5 time periods to the measurements for the last 5 time periods.

You may assume that heat flow is approximately normal for each group.

Time period 1 (Group 1): 9.273, 9.262, 9.243, 9.283, 9.270
Time period 2 (Group 2): 9.240, 9.292, 9.284, 9.279, 9.258

Unless otherwise stated, give your answers to three decimal places.

Construct a 95% confidence interval for the difference in mean heat flow. Give your answers to three decimal places. Use t∗=2.352t∗=2.352.
( , )
Conduct a hypothesis test to determine whether the average heat flow is higher in period 1 than period 2.
1. What is the parameter of interest?
  i. pp
  ii. μμ
  iii. p1−p2p1−p2
  iv. μ1−μ2μ1−μ2
  v. μdμd
2. What is the correct null value for this test?
3. What sign should appear in the alternative hypothesis?
  i. == ii. << iii. >> iv. ≠≠
4. The test statistic for this test is t=t= .
5. The p-value for this test is . Use df=7.194df=7.194. (If p-value <0.001<0.001, enter 0).
6. Select the appropriate decision for this hypothesis test (use α=0.01α=0.01).
  i. Reject H0H0 ii. Fail to reject H0H0 iii. Accept H0H0
7. Select the appropriate interpretation for this hypothesis test (use α=0.01α=0.01).
  i. We have statistically significant evidence to suggest that the average heat flow is lower in period 2 than 1.
  ii. We do not have statistically significant evidence to suggest that the average heat flow is lower in period 2 than 1.
  iii. We have statistically significant evidence to suggest that the average heat flow is the same in period 2 and period 1.
8. If an error had been made on this test, what kind of error would it have been?
  i. Type I error ii. Type II error