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# Confidence interval for true average

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Question: An article contained the following observations on degree of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range.

Degree: 429 421 421 422 425 427 431 436 437 439 446 447 448 452 453 463 465

a) Calculate a two-sided 98% confidence interval for true average degree of polymerization. What is the lower limit?

b) Calculate a two-sided 98% confidence interval for true average degree of polymerization. What is the upper limit?

c) Calculate a two-sided 95% confidence interval for true average degree of polymerization (as did the authors of the article).
What is the lower limit of this confidence interval?

d) Calculate a two-sided 95% confidence interval for true average degree of polymerization (as did the authors of the article).
What is the upper limit of this confidence interval?

e) Does the 95% confidence interval suggest that 440 is a plausible value for true average degree of polymerization?

f) Does the 95% confidence interval suggest that 450 is a plausible value?

Give your answers correct to three decimal places.

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#### Solution Preview

Question: An article contained the following observations on degree of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range.

Degree: 429 421 421 422 425 427 431 436 437 439 446 447 448 452 453 463 465

a) Calculate a two-sided 98% confidence interval for true average degree of polymerization. What is the lower limit?

b) Calculate a two-sided 98% confidence interval for true average degree of polymerization. What is the upper limit?

c) Calculate a two-sided 95% confidence interval for true average degree of polymerization (as did the authors of the article).
What is the lower limit of this confidence interval?

d) Calculate a two-sided 95% confidence interval for true average degree of polymerization (as did the authors of the article).
What is the upper limit of this confidence interval?

e) Does the 95% confidence interval suggest that 440 is a plausible value for true average degree of polymerization?

f) Does the 95% confidence interval suggest that 450 is a plausible value?

Answer:
Calculate the mean and standard deviation of the sample

Mean and standard deviation

X= X 2 =
...

#### Solution Summary

Calculates Confidence interval for true average degree of polymerization.

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