Question

1. Using the t​ tables, software, or a​ calculator, estimate the values asked for in parts​ (a) and​ (b) below.

​a) Find the critical value of t for a 90​% confidence interval with df=21.

​b) Find the critical value of t for a 99​% confidence interval with df=82.

2. For parts a and b​, use technology to estimate the following.

​a) The critical value of t for a 99​%confidence interval with df=1.

​b) The critical value of t for a 95​% confidence interval with df=106.

Answer 1

Solution :

a) degrees of freedom = 21

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

t/2,df = 1.721

b) degrees of freedom = 82

At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.005

t/2,df = 2.637

a) degrees of freedom = 1

At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.005

t/2,df = 63.657

b) degrees of freedom = 106

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

t/2,df = 1.983