Answer:
The required interval is [tex][12.0519,14.7481][/tex]
Step-by-step explanation:
Consider the provided information.
It is given that:
n = 1006, mean = 13.4 and s = 16.6
We need to construct a 99% confidence interval.
That means α = 0.01 and α/2 = 0.005
[tex]Z_{\alpha/2}=2.5758[/tex]
First find the standard error as shown:
[tex]SE=\frac{16.6}{\sqrt{1006}} =0.5234[/tex]
Now to calculate confidence interval calculate: [tex]Mean \pm Z_{\alpha/2} \times SE[/tex]
[tex]=13.4 \pm 2.5758 \times 0.5234[/tex]
[tex]=13.4 \pm 1.34817372[/tex]
[tex][12.0519,14.7481][/tex]
Hence, the required interval is [tex][12.0519,14.7481][/tex]
