Answer: (1500.66,1599.34)
Step-by-step explanation:
Confidence interval for population mean:
[tex]\overline{x}\pm z^*\dfrac{\sigma}{\sqrt{n}}[/tex]
,where [tex]\overline{x}[/tex] = Sample mean , n= Sample size, z* = critical two tailed z-value , [tex]\sigma[/tex] = population standard deviation.
As per given , we have
n= 16
[tex]\sigma = 154[/tex] square feet
[tex]\overline{x}= 1550[/tex] square feet
[tex]\alpha= 1-0.80 = 0.20[/tex]
Critical z-value = [tex]z_{\alpha/2}=z_{0.2/2}=z_{0.1}=1.2815[/tex]
Confidence interval for population mean:
[tex]1550\pm (1.2815)\dfrac{154}{\sqrt{16}}\\\\ = 1550\pm (1.2815)\dfrac{154}{4}\\\\= 1550\pm 49.33775\\\\ =(1550-49.33775,\ 1550+49.33775)\\\\\approx (1500.66,\ 1599.34)[/tex]
Required confidence interval: (1500.66,1599.34)
