Question

Conduct the following exercise by R. Also, when you verify the normality assumption in part (b) use both box-plot and normal probability

The article “Measuring and Understanding the Aging of Kraft Insulating Paper in Power Transformers” (IEEE Electrical Insul. Mag., 1996: 28–34) contained the following observations on degree of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range: 418 421 421 422 425 427 431 434 437 439 446 447 448 453 454 463 465 a. Construct a boxplot of the data and comment on any interesting features.
b. Is it plausible that the given sample observations were selected from a normal distribution?
c. Calculate a two-sided 95% confidence interval for true average degree of polymerization (as did the authors of the article). Does the interval suggest that 440 is a plausible value for true average degree of polymerization? What about 450?

Answer 1

a) By using R software we can find boxplot.

Enter data into R software.

R codes and output.

data<-c(418,421,421,422,425,427,431,434,437,439,446,447,448,453,463,465)

> boxplot(data)

We get boxplot

Comment: Data is normally distributed.

b) Yes, the given sample observations were selected from a normal distribution.

c) We have to calculate two-sided 95% confidence interval for the true average degree of polymerization.

Sample size = n = 17

Sample mean = \bar{x} = 438.2941

Standard deviation = s = 15.1442

We have to construct 95% confidence interval.

Formula is