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 18 observations.

b. A 99% confidence level and a sample of 18 observations.

c. A 95% confidence level and a sample of 9 observations.

d. A 99% confidence level and a sample of 9 observations.

Answer 1

Solution :

We know that df = n-1

a. A 95% confidence level and a sample of 18 observations.

α = 1-0.95 = 0.05

tα/2 = 2.110 , df = n-1 = 17

b. A 99% confidence level and a sample of 18 observations.

α = 1-0.99 = 0.01

tα/2 = 2.898, df = n-1 = 17

c. A 95% confidence level and a sample of 9 observations.

α = 1-0.95 = 0.05

tα/2 = 2.306, df = n-1 = 8

d. A 99% confidence level and a sample of 9 observations.

α = 1-0.99 = 0.01

tα/2 = 3.355, df = n-1 =8