Question 1197083
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Enter the given data into a spreadsheet.
Let's say the upper left corner is in cell A1
That places the bottom right corner in cell F6


In another blank cell off to the side somewhere, type in <font color=blue>=AVERAGE(A1:F6)</font> to find the arithmetic mean of this data set.
Don't forget about the equal sign up front.
The result should be roughly 2.819444
This is the sample mean xbar.


If you wanted to find the value of xbar another way, then add up all the values and divide by 36 since there are 6*6 = 36 items in this list.
The values add up to 101.5 which leads to xbar = 101.5/36 = 2.819444
The command <font color=blue>=SUM(A1:F6)</font> will add up the values in cells A1 to F6.


At 99% confidence, the z critical value is roughly z = 2.576
Use a table like this
<a href = "https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf">https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf</a>
to get that value. Look at the bottom row labeled "Z" and above the 99% confidence level.


An alternative way to calculate this critical value is to type <font color=blue>=NORMINV((1-0.99)/2, 0, 1)</font> into the spreadsheet.
The portion (1-0.99)/2 represents the area in each tail at 99% confidence.
The spreadsheet should display -2.5758293035489, but we'll go with the positive version of that number.



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We have this information
z = 2.576 = critical value
xbar = 2.819444 = approximate sample mean
sigma = 0.62 = given population standard deviation
n = 36 = sample size


Let's compute the margin of error
E = z*sigma/sqrt(n)
E = 2.576*0.62/sqrt(36)
E = 0.266187


So,
L = lower boundary
L = xbar - E
L = 2.819444 - 0.266187
L = 2.553257
L = 2.55
and
U = upper boundary
U = xbar + E
U = 2.819444 + 0.266187
U = 3.085631
U = 3.09


The 99% confidence interval for the population mean mu is roughly (2.55, 3.09)
This is in the format (L, U)


This can be expressed as 2.55 < mu < 3.09 which is in the format L < mu < U


A third alternative is to say {{{2.819444 +-  0.266187}}} which is in the format {{{xbar +- E}}}


Round each value according to the instructions your teacher provides.
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