question below

Question

What would be the critical value for an 80% confidence interval of the mean? (Assume the data
is normally distributed, the population standard deviation  is not known, and the sample size is
n = 40.)

Answer 1

This is a question in which you would usually use a table to find the answer. You can use the normal distribution or z tables from the back of most textbooks to find the appropriate cutoff. 

 

Here's  a link to a basic table. 

 

http://uregina.ca/~gingrich/tt.pdf

 

You should use the Confidence Interval columns at the top to select the right column. Then look on the left for your degrees of freedom (n-1). In this case 39 is not represented on the table, although 40 will provide a very close estimate. 

 

The cutoff for 39 degrees of freedom is 1.303639

The cutoff for 40 degrees of freedom is 1.303077

 

So if you are only carrying to two decimal places, these values are effectively the same. 

 

As you can see the value provided on the table is 1.303 for 40 degrees of freedom.