Question

Wear-out of used display panels. Refer to Exercise 4.126 (p. 270) and the study of the wear-out failure time of used colored display panels purchased by an outlet store. Recall that prior to acquisition, the panels had been used for about one-third of their expected lifetimes. The failure times (in years) for a sample of 50 used panels are reproduced in the table. An SPSS printout of the analysis is shown below.

a. Locate a 95% confidence interval for the true mean failure time of used colored display panels on the printout.

b. Give a practical interpretation of the interval, part a.

c. In the repeated sampling of the population of used colored display panels, where a 95% confidence interval for the mean failure time is computed for each sample, what proportion of all the confidence intervals generated will capture the true mean failure time?

Short answer

1. $(1.6776,2.1924)$
   

   
   
2. We can say that the mean failure time lies between (1.6776,2.1924) 95% time
3. 0.95
   

Step-by-step solution

(a) Calculating Confidence Interval

From the given output, 95% confidence interval for the true mean failure time of used colored display panels: $(1.6776,2.1924)$.

(b) Practical Interpretation

We are 95% confident that the true mean failure time of used colored display time of used colored display panels lies within $(1.6776,2.1924)$

(c) Calculating proportions of Confidence Intervals

Suppose we were to take many different samples and compute a 95% confidence interval for each sample. In that case, the proportion of all the confidence intervals generated will capture the true mean failure time is approximately 0.95.