Question 1210349
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I recommend using a spreadsheet for this type of problem. 
If you want to use a TI83 or similar, then refer to the next section below.


Copy/paste the given data into a spreadsheet. 
Let's say the upper left corner goes in cell A1.
This would have the lower right corner in cell H2.


In some other blank cell, say cell A4, we'll have the following command
<font color=blue>=Average(A1:H2)</font>
Don't forget about the equal sign up front. Otherwise the spreadsheet command will not execute.
This computes the arithmetic mean of the values from cell A1 to H2. 
The result of this calculation is 19 exactly. 
This is the value of xbar, which is the sample mean.


Now move to cell A5.
Type this in, or copy/paste
<font color=blue>=Confidence.T(1-0.9,Stdev(A1:H2),Count(A1:H2))</font>
The Confidence function produces the margin of error needed.
The "dot T" portion tells the spreadsheet to do the T distribution version. Otherwise, it defaults to the normal distribution.
We use the T distribution for two reasons: we don't know the value of sigma, and n = 16 doesnt make n > 30 true


The 3 parameters of the confidence function are:
alpha = significance level = 1-C = 1-0.90 = 0.10
stdev = standard deviation
n = sample size = number of values
You can manually type in the number of values (16), or use the Count function.


The result of the Confidence calculation is roughly 1.63200106504704, which is the approximate margin of error.


In cells A6 and A7 will be the following commands
<font color=blue>=A4-A5</font> 	
<font color=blue>=A4+A5</font>
They represent the lower and upper bounds of the confidence interval.
The results of the calculations are roughly <font color=red>17.367998934953 and	20.632001065047</font>


When rounding to 3 decimal places we get the confidence interval <font color=red>(17.368, 20.632)</font> 
Your final answer will vary depending how your teacher wants you to round.


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If you want to use a TI83 or similar, then follow these steps.


Press the button labeled "STAT". Then select "Edit".
This brings up the data tables. Clear out list L1 if it has values in it already.
Once fully empty, enter the data values into the list. 


After the data is entered, quit to the home screen. 
Press the STAT button again. Scroll to right to land on "Tests". Hit enter.
Scroll down until reaching "T-intveral". It's the 8th item of the list. Hit enter.


The input will be "data". The specific data is inside list L1.
The "freq" or "frequency" will be set to 1.
The C-level, aka confidence level, is set to 0.90
Scroll down to "calculate", and hit enter, to have the approximate interval <font color=red>(17.368, 20.632)</font> show up.
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