How well materials conduct heat matters when designing houses, for example. Cond
ID: 3151355 • Letter: H
Question
How well materials conduct heat matters when designing houses, for example. Conductivity is measured in terms of watts of heat power transmitted per square meter of surface per degree Celsius of temperature difference on the two sides of the material. In these units, glass has conductivity about 1. The National Institution of Standards and Technology provides exact data on properties of materials. Here are 11 measurements of the heat conductivity of a particular type of glass.
1.11 1.06 1.12 1.06 1.12 1.08 1.09 1.16 1.16 1.17 1.14
(a) We can consider this an SRS of all specimens of glass of this type. Make a stemplot. (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.)
Is there any sign of major deviation from Normality?
The stemplot shows that the data are not skewed and have no outliers.The stemplot shows that the data is skewed to the left with one outlier. The stemplot shows that the data is skewed to the right with one outlier.
(b) Give a 99% confidence interval for the mean conductivity. (Use 3 decimal places.)
( , )
Explanation / Answer
a)
Sorting,
1.06
1.06
1.08
1.09
1.11
1.12
1.12
1.14
1.16
1.16
1.17
Hence,
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The stemplot shows that the data are not skewed and have no outliers. [ANSWER]
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B)
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 = 0.005
X = sample mean = 1.115454545
t(alpha/2) = critical t for the confidence interval = 3.169272673
s = sample standard deviation = 0.039588795
n = sample size = 11
df = n - 1 = 10
Thus,
Lower bound = 1.077624614
Upper bound = 1.153284477
Thus, the confidence interval is
( 1.077624614 , 1.153284477 ) [ANSWER]
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