Question 1206353
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Answer: <font color=red>(32.804, 38.396)</font>
It is equivalent to writing 32.804 < mu < 38.396


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Explanation


n = 13 = sample size
xbar = 35.6 = sample mean
s = 3.3 = sample standard deviation
sigma = population standard deviation = unknown


Because we don't know the value of sigma, and because n > 30 is not the case, we must use the T distribution.


df = degrees of freedom
df = n-1
df = 13-1
df = 12


Use a T table such as this one
<a href="https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf">https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf</a>
or one found on any other websites, or one found in the back of your stats textbook.
For exam purposes, your teacher is likely to hand out such a table if s/he expected you to use it.


Locate the row that starts with df = 12.
The column we want will have "confidence level = 99%" labeled at the bottom. 
The intersection of this row and column leads to 3.055 which is the approximate t critical value.
It means that P(-3.055 < T < 3.055) = 0.99 approximately when df = 12.


Many online stats calculators can be used as an alternative to determine the t critical value.
Or you could use a TI84 or similar
<a href="https://www.statology.org/how-to-find-the-t-critical-value-on-a-ti-84-calculator/">https://www.statology.org/how-to-find-the-t-critical-value-on-a-ti-84-calculator/</a>


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Here are the key values we need
xbar = 35.6
s = 3.3 
n = 13
t = 3.055 (approximate)


Then,
E = margin of error
E = t*s/sqrt(n)
E = 3.055*3.3/sqrt(13)
E = 2.796105
which is approximate


Now we can compute the lower bound and upper bound.
L = lower bound
L = xbar - E
L = 35.6 - 2.796105
L = 32.803895
L = 32.804


U = upper bound
U = xbar + E
U = 35.6 + 2.796105
U = 38.396105
U = 38.396


The 99% confidence interval of the form L < mu < U would be roughly 32.804 < mu < 38.396
That condenses to the notation (32.804, 38.396)


Some textbooks will use the notation [32.804, 38.396] which represents the same thing more or less.
The fact we include endpoints or not isn't really important to the confidence interval overall.


Here is a calculator you can use to check your work
<a href="https://www.socscistatistics.com/confidenceinterval/default2.aspx">https://www.socscistatistics.com/confidenceinterval/default2.aspx</a>
and here's another similar resource
<a href="https://www.statology.org/confidence-intervals-ti-84-calculator/">https://www.statology.org/confidence-intervals-ti-84-calculator/</a>
The function you want is called <font color=red>TInterval</font>
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