Question 1207888
<font color=black size=3>
n = 20 = sample size
xbar = 5.2 = sample mean
s = 3.05 = sample standard deviation
sigma = population standard deviation = unknown


We don't know the value of sigma and n > 30 is not the case, so we must use the T distribution.
df = degrees of freedom
df = n-1
df = 20-1
df = 19

 
You could use a stats calculator like a TI83 to find the T critical value.
However, I'll use a T table such as this
<a href="https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf">https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf</a>
Such a table can be found at the back of your stats textbook.
Highlight the df = 19 row and the column that mentions "confidence level = 95%" (mentioned at the bottom of the table)
The intersection of this row and column yields the approximate t critical value t = <font color=red>2.093</font>


What does this tell us?
It tells us that P(-2.093 < t < 2.093) = 0.95 approximately when df = 19.
The 0.95 is the area of the main body while 1-0.95 = 0.05 is the combined area of the two tails.
The 0.95 refers to the confidence level 95%.



The final answer is <font color=red>option A</font>
</font>