Question

You intend to estimate a population mean with a confidence interval. You believe the population to have a normal distribution. Your sample size is 9.

Find the critical value that corresponds to a confidence level of 98%. Report answer accurate to three decimal places with appropriate rounding.

Answer 1

Solution:

Given:

Sample Size = n = 9

c = confidence level = 98%

We have to find critical value that  corresponds to a confidence level of 98%.

Since sample size is small and population standard deviation is unknown, we use t distribution to find critical value.

Find :

df = n - 1

df = 9 - 1

df = 8

and

two tail area = 1 -c = 1 - 0.98 = 0.02

Thus look in t table for df = 8 and two tail area = 0.02 and find corresponding t critical value.

From above table we can see t critical value corresponding to df = 8 and two tail area = 0.02 is: 2.896

That is:

t critical value = 2.896