IE 300 / GE 331 Discussion Problem Set 11
•
810
𝑛𝑛
= 10,
𝑥𝑥̅
= 1.5045,
𝜎𝜎
= 0.01,
𝑧𝑧
0.005
= 2.58
The 99% confidence interval on the mean hole diameter is
𝑥𝑥̅ − 𝑧𝑧
0.005
𝜎𝜎
√𝑛𝑛
≤ 𝜇𝜇 ≤ 𝑥𝑥̅
+
𝑧𝑧
0.005
𝜎𝜎
√𝑛𝑛
→
1.4963
≤ 𝜇𝜇 ≤
1.5127.
•
822
a)
𝑡𝑡
0.05,14
= 1.761
b)
𝑡𝑡
0.01,19
= 2.539
c)
𝑡𝑡
0.001,24
= 3.467
•
832
a)
The data appear to be approximately normally distributed based on the qq plot below which exhibits a
reasonably straight line.
b)
𝑛𝑛
= 6,
𝑥𝑥̅
= 16.98,
𝑠𝑠
= 0.319,
𝑡𝑡
0.005,5
= 4.032
Note that we should use the tdistribution since the data appear to be approximately normal, variance of
the population is unknown, and the sample size is small. The 99% confidence interval on the mean is
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IE 300 / GE 331 Discussion Problem Set 11
𝑥𝑥̅ − 𝑡𝑡
0.005,5
𝑠𝑠
√𝑛𝑛
≤ 𝜇𝜇 ≤ 𝑥𝑥̅
+
𝑡𝑡
0.005,5
𝑠𝑠
√𝑛𝑛
→
16.455
≤ 𝜇𝜇 ≤
17.505.
We are 99% confident (NOT PROBABILITY) that the true mean lies within this interval.
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 Spring '09
 NegarKayavash
 Normal Distribution, Standard Deviation

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