Compute 95% and 99% confidence intervals for µ using Method 1 with a Student's t distribution!

Question

When σ is unknown and the sample is of size n ≥ 30, there are two methods for computing confidence intervals for μ.

Method 1: Use the Student's t distribution with d.f. = n − 1.
This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method.

Consider a random sample of size n = 36, with sample mean x = 44.2 and sample standard deviation s = 5.9.(a) Compute 95% and 99% confidence intervals for μ using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal.

95%
lower limit?    

upper limit?   

 

99%

lower limit?

 

upper limit? 

Answer 1

95% confidence interval = [x-t*s/√n, x+t*s/√n] = [44.2-2.021*5.9/√36, 44.2+2.021*5.9/√36]=[42.21, 46.19]

 

99% confidence interval = [44.21-2.704*5.9/√36, 44.21-2.704*5.9/√36]=[41.55, 46.87]