A simple random sample is drawn from a population that is known to be normally distributed. The sample variance, s2, is determined to be 12.6 Construct a 90\% confidence interval for \sigma if the sample size, n, is 20 and construct a 90\% confidence interval for \sigma if the sample size, n, is 30.

UkusakazaL 2021-08-02 Answered
A simple random sample is drawn from a population that is known to be normally distributed. The sample variance, s2, is determined to be 12.6
A. Construct a 90% confidence interval for σ if the sample size, n, is 20. (Hint: use the result obtained from part (a)) 7.94 (LB) & 23.66 (UB))
B. Construct a 90% confidence interval for σ if the sample size, n, is 30. (Hint: use the result obtained from part (b)) 8.59 (LB) &amp. 20.63 (UB)
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Answers (1)

question2answer
Answered 2021-08-17 Author has 155 answers

Step 1
Here σ2=12.6 and c=90% which is 0.9.
Therefore 1c2=10.92=0.05 and 1(1c2)=0.95
Part A
For n=20 the degrees of freedom are:
df=201=19
So the χ squared table values are:
X0.95=10.117 and X0.05=30.144
So the upper and lower bounds are given by:
UB=(1910.117)(12.6)
UB=23.66
LB=(1930.144)(12.6)
LB=7.94
Part B
For n=30 the degrees of freedom are:
df=301=29
So the χ squared table values are:
X0.95=17.708 and X0.05=42.557
So the upper and lower bounds are given by:
UB=(2917.708)(12.6)
UB=20.63
LB=(2942.557)(12.6)
LB=8.59

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