Answer:
The population mean is 19.2 to 20.8.
Step-by-step explanation:
The formula of Confidence interval is
CI = mean ± z*[tex]\frac{s}{\sqrt{n} }[/tex]
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*[tex]\frac{4.8}{\sqrt{144} }[/tex]
= 20 ± 2*[tex]\frac{4.8}{12}[/tex]
= 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.
