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 tα/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 95% confidence level and a sample of 22 observations.

b.A 99% confidence level and a sample of 22 observations.

c.A 95% confidence level and a sample of 14 observations.

d.A 99% confidence level and a sample of 14 observations.

Answer 1

For a two tailed test for given confidence level and sample size

df = sample size - 1

a.A 95% confidence level and a sample of 22 observations.

= 0.05

df = 22 - 1 = 21

t = 2.0796

b.A 99% confidence level and a sample of 22 observations.

= 0.01

df = 22 - 1 = 21

t = 2.8314

c.A 95% confidence level and a sample of 14 observations.

= 0.05

df = 14 - 1 = 13

t = 2.1604

d.A 99% confidence level and a sample of 14 observations.

= 0.01

df = 14 - 1 = 13

t =  3.0123