STATISTICS 11

Question

Construct a confidence interval for the population mean using a t-distribution:

c = 95% m = 17.3 s = 4.1 n = 10

Answer 1

There are n-1 = 9 degrees of freedom. The two tails will have a total of 5% probability, so each has 2.5%. Thus look up the critical value t^* such that P(T<t) = 0.975 on the t_df=9 distribution. Most books have a table and looking it up you have:

 

t^* ≈ 2.262

 

Also the standard error is:

 

SE = s/√n = 4.1/√10 ≈ 1.297

 

Thus the 95% confidence interval is:

 

CI = x_bar ± t^* SE ≈ 17.3 ± (2.262)(1.297) ≈ (14.4,20.2)