I have a question: You intend to estimate a population mean displaystylemu with the following sample. 54.7 48.9 56.3 43.5 41.5 41.2 54.2 You believe t

Reeves 2021-02-11 Answered
I have a question:
You intend to estimate a population mean μ with the following sample.
54.7
48.9
56.3
43.5
41.5
41.2
54.2
You believe the population is normally distributed. Find the 99.9% confidence interval. Enter your answer as an open-interval (i.e., parentheses) accurate to twp decimal places (because the sample data are reported accurate to one decimal place).
99.9%C.I.=(35.68,61.54)Incorrect
Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.
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Expert Answer

Delorenzoz
Answered 2021-02-12 Author has 91 answers
Step 1
Given information-
Sample size, n=7
Calculating sample mean and sample standard deviation using excel.
=AVERAGE(54.7:54.2)
And standard deviation-
=STDEV.S(54.7:54.2)
Sample mean, x=48.61429
Sample standard deviation, s=6.571765
Confidence level, c=0.999
So, significance level, α=0.001
Since here population standard deviation is unknown so we will use t-distribution.
Now, degree of freedom is given by-
Degree of freedom, df=n1
Degree of freedom, df=71=6
Step 2
Now, 99.9% confidence interval is given by
Confidence interval =x±tα2,n1×sn
So, t-critical is given by
t0.0012,71=5.959(From excel using formula=T.INV.2T(0.001,6))
C.I.=48.61429±5.959×6.5717657
C.I=(33.81,63.42)
So, 99.9% confidence interval is 33.81 to 63.42
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