We use the t distribution for the statistical inference of the population mean w

Question

We use the t distribution for the statistical inference of the population mean when the underlying population standard deviation is not known. Under the assumption that the population is normally distributed, find t^af for the following scenarios. Use Table 2. (Round your answers to 3 decimal places.) A 95% confidence level and a sample of 16 observations. A 90% confidence level and a sample of 16 observations. A 95% confidence level and a sample of 7 observations. A 90% confidence level and a sample of 7 observations.

Explanation / Answer

a)

As c = 0.95,

alpha/2 = (1-c)/2 = 0.025

and

df = n - 1 = 15

Then by table,

tcrit = 2.131 [ANSWER]

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b)

As c = 0.90,

alpha/2 = (1-c)/2 = 0.05

and

df = n - 1 = 15

Then by table,

tcrit = 1.753 [ANSWER]

*************************

C)

As c = 0.95,

alpha/2 = (1-c)/2 = 0.025

and

df = n - 1 = 6

Then by table,

tcrit = 2.447 [ANSWER]

***********************

d)

As c = 0.90,

alpha/2 = (1-c)/2 = 0.05

and

df = n - 1 = 6

Then by table,

tcrit = 1.943 [ANSWER]

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