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.)

		tα/2,df
a.	A 90% confidence level and a sample of 11 observations.
b.	A 95% confidence level and a sample of 11 observations.
c.	A 90% confidence level and a sample of 24 observations.
d.	A 95% confidence level and a sample of 24 observations.

Answer 1

a.A 90% confidence level and a sample of 11 observations.:

level of significance =0.1

   df=11-1=10

t_α/2,10=1.81

b.A 95% confidence level and a sample of 11 observations.:

level of significance =0.05

df=11-1=10

t_α/2,10=2.23

c.A 90% confidence level and a sample of 24 observations:

level of significance =0.1

   df=24-1=23

t_α/2,23=1.71

d.A 95% confidence level and a sample of 24 observations

level of significance =0.05

   df=24-1=23

t_α/2,23=2.07