Question

We use the t distribution to construct a confidence interval for the population mean when the underlying population standard deviation is not known. Under the assumption that the population is normally distributed, find t_α/2,df for the following scenarios. (You may find it useful to reference the t table. Round your answers to 3 decimal places.)

a.	A 90% confidence level and a sample of 21 observations.
b.	A 95% confidence level and a sample of 21 observations.
c.	A 90% confidence level and a sample of 13 observations.
d.	A 95% confidence level and a sample of 13 observations.

Answer 1

a

Degrees of freedom = df = n - 1 =21 - 1 = 20

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,20 = 1.725 ( using student t table)

.

b

n = Degrees of freedom = df = n - 1 = 21- 1 = 20

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,20 = 2.086 ( using student t table)

c.

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,12 = 1.782 ( using student t table)

d.

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,12 = 2.179 ( using student t table)