Question

A random sample of 144 observations has a mean of 20. The population standard deviation is known to equal 4.8. The 95.44% confidence interval for the population mean is

Answer 1

Answer:

The population mean is 19.2 to 20.8.

Step-by-step explanation:

The formula of Confidence interval is

CI = mean ± z*$\frac{s}{\sqrt{n} }$

where

n = sample size

s  = Population standard deviation.

mean = Sample mean

z(α/2) = Two tailed z-value for significance level of .

Given : Confidence level = 95.44% = 0.9544

Significance level =  α = 1-0.9544 = 0.0456

Now we Use standard z-value table  

z-value for Significance level of 0.0456 :

z(α/2) = z(0.0228) = 1.99 = 2(approximately)

And we are given

n=144

s = 4.8

mean = 20

so the required Confidence interval is

CI = 20± 2*$\frac{4.8}{\sqrt{144} }$

     = 20 ± 2*$\frac{4.8}{12}$

      = 20 ± (0.8)

      = (20-0.8, 20+0.8 )

       = (19.2 , 20.8)

Therefore the 95.44% CI value  for the population mean of 20 is 19.2 to 20.8.