In: Math
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.
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