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 90% confidence level and a sample of 25 observations.

b. A 95% confidence level and a sample of 25 observations.

c. A 90% confidence level and a sample of 19 observations.

d. A 95% confidence level and a sample of 19 observations.

Answer 1

Solution:

a)

Given:

Confidence level = 0.90

So, level of significance = = 0.10

Sample size = n = 25

Degrees of freedom = df = n-1 = 25-1 = 24

We have to find t_α/2 = ...?

We can use t-table or excel function.

Using excel function, =TINV(0.1,24)

t_α/2 = 1.711

b)

Given:

Confidence level = 0.95

So, level of significance = = 0.05

Sample size = n = 25

Degrees of freedom = df = n-1 = 25-1 = 24

We have to find t_α/2 = ...?

We can use t-table or excel function.

Using excel function, =TINV(0.05,24)

t_α/2 = 1.064

c)

Given:

Confidence level = 0.90

So, level of significance = = 0.10

Sample size = n = 19

Degrees of freedom = df = n-1 = 19-1 = 18

We have to find t_α/2 = ...?

We can use t-table or excel function.

Using excel function, =TINV(0.1,18)

t_α/2 = 1.734

d)

Given:

Confidence level = 0.95

So, level of significance = = 0.10

Sample size = n = 19

Degrees of freedom = df = n-1 = 19-1 = 18

We have to find t_α/2 = ...?

We can use t-table or excel function.

Using excel function, =TINV(0.1,18)

t_α/2 = 2.101

Done