Question

The number of square feet per house is normally distributed with a population standard deviation of 154 square feet and an unknown population mean. If a random sample of 16 houses is taken and results in a sample mean of 1550 square feet, find a 80% confidence interval for the population mean. Round your answer to TWO decimal places.

Answer 1

Answer: (1500.66,1599.34)

Step-by-step explanation:

Confidence interval for population mean:

$\overline{x}\pm z^*\dfrac{\sigma}{\sqrt{n}}$

,where $\overline{x}$ = Sample mean , n= Sample size, z* = critical two tailed z-value , $\sigma$ = population standard deviation.

As per given , we have

n= 16

$\sigma = 154$ square feet

$\overline{x}= 1550$ square feet

$\alpha= 1-0.80 = 0.20$

Critical z-value = $z_{\alpha/2}=z_{0.2/2}=z_{0.1}=1.2815$

Confidence interval for population mean:

$1550\pm (1.2815)\dfrac{154}{\sqrt{16}}\\\\ = 1550\pm (1.2815)\dfrac{154}{4}\\\\= 1550\pm 49.33775\\\\ =(1550-49.33775,\ 1550+49.33775)\\\\\approx (1500.66,\ 1599.34)$

Required confidence interval:  (1500.66,1599.34)