Ex 6.14 modified as follows: In a random sample of 55 panels, the average failure time is 2.07 years and the standard deviation is 1.11 years. Find the 91.7% CI for the population mean failure time **Problem Statement:**1. **Ex 6.14 Modified:** - In a random sample of 55 panels, the average failure time is 2.07 years, and the standard deviation is 1.11 years. Find the 91.7% Confidence Interval (CI) for the population mean failure time.**Excerpt from Textbook:**- **CHAPTER 6: Inferences Based on a Single Sample.** - **6.14 Wear-out of Used Display Panels:** - Refer to Exercise 4.126 (p. 247) regarding the study of wear-out failure time of used colored display panels bought by an outlet store. The failure times (in years) for a sample of 50 used panels are provided in a table. An XLSTAT output of the analysis is displayed. - **Tasks:** - **a.** Locate a 95% confidence interval for the true mean failure time of used colored display panels. - **b.** Provide a practical interpretation of the interval from part a. - **c.** In repeated sampling of the population of used colored display panels, determine the proportion of all confidence intervals that would capture the true mean failure time if computed at 95% confidence.- **Data Table (Failure Times):** - A table listing failure times in years for individual panels, ranging from 0.01 to 3.50.- **XLSTAT Output:** - Summary statistics for "FailTime": - **Observations:** 50 - **Minimum:** 0.0100 - **Maximum:** 3.500 - **Mean:** 1.9350 - **Standard Deviation:** 0.9287 - **95% Confidence Interval on the Mean:** [1.6776, 2.1924]**Source Information:**- Based on a paper "A Weibull Wearout Test: Full Bayesian Approach," presented at the Mathematical Sciences Colloquium in Binghamton, UK, December 2001.**Discussion:**- The exercise involves computing and interpreting confidence intervals, which are estimates of a population parameter based on a sample statistic. The context is a practical scenario involving wear-out times of display panels.

Given: n = 55 X = 2.07 s = 1.11 Confidence level = 91.7% Formula Used: Confidence interval = X ± tsn

Answered: modified as follows: In a random sample…

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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Ex 6.14 modified as follows: In a random sample of 55 panels, the average failure time is 2.07 years and the standard deviation is 1.11 years. Find the 91.7% CI for the population mean failure time

**Problem Statement:**

1. **Ex 6.14 Modified:**
- In a random sample of 55 panels, the average failure time is 2.07 years, and the standard deviation is 1.11 years. Find the 91.7% Confidence Interval (CI) for the population mean failure time.

**Excerpt from Textbook:**

- **CHAPTER 6: Inferences Based on a Single Sample.**

- **6.14 Wear-out of Used Display Panels:**
- Refer to Exercise 4.126 (p. 247) regarding the study of wear-out failure time of used colored display panels bought by an outlet store. The failure times (in years) for a sample of 50 used panels are provided in a table. An XLSTAT output of the analysis is displayed.

- **Tasks:**
- **a.** Locate a 95% confidence interval for the true mean failure time of used colored display panels.
- **b.** Provide a practical interpretation of the interval from part a.
- **c.** In repeated sampling of the population of used colored display panels, determine the proportion of all confidence intervals that would capture the true mean failure time if computed at 95% confidence.

- **Data Table (Failure Times):**
- A table listing failure times in years for individual panels, ranging from 0.01 to 3.50.

- **XLSTAT Output:**
- Summary statistics for "FailTime":
- **Observations:** 50
- **Minimum:** 0.0100
- **Maximum:** 3.500
- **Mean:** 1.9350
- **Standard Deviation:** 0.9287
- **95% Confidence Interval on the Mean:** [1.6776, 2.1924]

**Source Information:**
- Based on a paper "A Weibull Wearout Test: Full Bayesian Approach," presented at the Mathematical Sciences Colloquium in Binghamton, UK, December 2001.

**Discussion:**
- The exercise involves computing and interpreting confidence intervals, which are estimates of a population parameter based on a sample statistic. The context is a practical scenario involving wear-out times of display panels.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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