Question

Researchers are interested in the mean age of a certain population. Let us say that they are asking the following questions: can we conclude that the mean age of this population is different from 30 years? If the sample mean of 10 individuals drawn from that population is 27and the population variance is 20. Make a confidence interval of the mean

	A.	1.96 , -1.96
	B.	24.23 ,29.20
	C.	24.23 , 29.77
	D.	2.77 , -2.77

Answer 1

Solution:

Given:

Sample size = n = 10

Sample mean =

Population variance =

then Population Standard Deviation = .

We have to find confidence interval of the mean.

Since confidence level is not given, we use 95% confidence level

where

We need to find z_c value for c=95% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.95) /2 = 1.95 / 2 = 0.9750

Look in z table for Area = 0.9750 or its closest area and find z value.

Area = 0.9750 corresponds to 1.9 and 0.06 , thus z critical value = 1.96

That is : Z_c = 1.96

Thus

thus

C. 24.23 , 29.77