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

Reeves

Answered question

2021-02-11

I have a question: 
With the given sample, you want to calculate the population mean μ.
54.7 
48.9 
56.3 
43.5 
41.5 
41.2 
54.2 
You think the population is dispersed normally. Find the 99.99 percent confidence level range. Put your response in parenthesis as an open-interval that is accurate to two 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.

Answer & Explanation

Delorenzoz

Delorenzoz

Skilled2021-02-12Added 91 answers

Step 1 
Given information- 
Sample size, n=7 
Excel is used to compute the sample mean and sample standard deviation.
=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 
We shall employ the t-distribution because the population's standard deviation is unknown here.

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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