You randomly select and weigh 27 samples of an allergy medication. The sample standard deviation is 1.22 milligrams. Assuming the weights are normally distributed, construct 90% confidence intervals for the population variance and standard deviation. Please interpret your result.

Tammy Todd 2020-12-15 Answered
You randomly select and weigh 27 samples of an allergy medication. The sample standard deviation is 1.22 milligrams. Assuming the weights are normally distributed, construct 90% confidence intervals for the population variance and standard deviation. Please interpret your result.
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Expert Answer

Demi-Leigh Barrera
Answered 2020-12-16 Author has 97 answers

Step 1
From the given information, S=1.22 milligrams and n=27.
The level of confidence is 0.90.
1α=0.90
α=10.90
α=0.10
Step 2
Then, a 90% interval for the population variance is
CI=((n1)S2X1an,n12<σ2<(n1)S2Xan,n12)
=((271)1.222X10.102,2712<σ2<(271)1.222X0.102,2712)
=(26×1.222X0.95,262<σ2<26×1.222X0.5,262)
=(26×1.22238.855<σ2<26×1.22215.379)
=(0.9952<σ2<2.5163)
Interpretation:
There is 90% confidence that the population variance lies between 0.9952 and 2.5163.
Step 3
The 90% confidence interval for the population standard deviation is
CI=((n1)S2X1an,n12<σ<(n1)S2Xan,n12)
=((271)1.222X10.102,271<σ<(271)1.222X0.102,2712)
=(26×1.222X0.95,262<σ<26×1.222X0.05,262)
(26×1.22238.885<σ<26×1.22215.379) [(Using excel function), (=CHISQ.INV(0.95,26)),

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