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)

Explanation:

Confidence interval for population mean:

`\overline{x}\pm z^*(\sigma)/(√(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)(154)/(√(16))\\\\ = 1550\pm (1.2815)(154)/(4)\\\\= 1550\pm 49.33775\\\\ =(1550-49.33775,\ 1550+49.33775)\\\\\approx (1500.66,\ 1599.34)`

Required confidence interval: (1500.66,1599.34)