Question

A sample of 25 observations is selected from a normal population where the population standard deviation is 20 and the sample meanis 120 Calculate the Lower Limit of the 70% confidence interval of the population mean Reminders You only need to calculate the Lower Limit of the confidence interval

Answer 1

Given , sample size = n = 25

Sample mean = 120

Population standard deviation = $\sigma$ = 20

We have to find lower limit of confidence interval.

Formula :

Lower limit =

T - 2a/2 X n

Where ,    is critical value for given confidence level  

-a/2

Confidence level = 70% = 0.7

Significance level = $\alpha$ = 1 - 0.7 = 0.3 ,  $\alpha$/2 = 0.15

So, critical value is ,  
-a/2
=
0.15
= 1.0364 ----> Using Excel function , "=NORMSINV(1-0.15)"=1.0364

Therefore, Lower limit of 70% confidence interval is given by,

Lower limit = 120 - 1.0364*(20/ )

25

Lower limit = 120 - 4.1456

Lower limit =115.854