An article contained the following observations on degree of polymerization for

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: (a) Construct a boxplot of the data. Comment on any interesting features. (Select all that apply.) There is little or no skew. There is one outlier. The data appears to be centered near 428. There are no outliers. The data appears to be centered near 438. The data is strongly skewed. (b) Is it plausible that the given sample observations were selected from a normal distribution? Yes No (c) Calculate a two-sided 95% confidence interval for true average degree of polymerization. (Round your answers to two decimal places.) (,) Does the interval suggest that 433 is a plausible value for true average degree of polymerization? Yes No Does the interval suggest that 450 is a plausible value? Yes No

Explanation / Answer

a)

Here,

Min = 418
Q1 = median of lower half = 426
Median = 436
Q3 = median of upper half = 449
Max = 465

Thus, the correct plot is

OPTION B. [ANSWER]

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A-2.

A. There is little or no skew.

E. The data appears to be centered near 438.

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b)

Yes, as there is little skew and no outliers.

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c)

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    438.2352941          
t(alpha/2) = critical t for the confidence interval =    2.119905299          
s = sample standard deviation =    14.72467916          
n = sample size =    17          
df = n - 1 =    16          
Thus,              
              
Lower bound =    430.6645627          
Upper bound =    445.8060256          
              
Thus, the confidence interval is              
              
(   430.6645627   ,   445.8060256   ) [ANSWER]

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YES, AS 433 IS INSIDE THIS INTERVAL.
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NO, AS 450 IS NOT INSIDE THIS INTERVAL.

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