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. z0.10 z0.05 z0.025 z0.01 z0.005 1.282 1.645 1.960 2.326 2.576 You may use a calculator or the common z values above.

Answer 1

(1500.64, 1599.36) this is the correct answer

Answer 2

The 80% confidence interval for the population mean is between 1500 square feet and 1600 square feet.

Explanation:

We have that to find our
`\alpha` level, that is the subtraction of 1 by the confidence interval divided by 2. So:

`\alpha = (1-0.8)/(2) = 0.1`

Now, we have to find z in the Ztable as such z has a pvalue of
`1-\alpha`.

So it is z with a pvalue of
`1-0.1 = 0.9`, so
`z = 1.282`

Now, find M as such

`M = z*(\sigma)/(√(n))`

In which
`\sigma` is the standard deviation of the population and n is the size of the sample.

`M = 1.282*(156)/(√(16)) = 50`

The lower end of the interval is the sample mean subtracted by M. So it is 1550 - 50 = 1500 square feet.

The upper end of the interval is the sample mean added to M. So it is 6.4 + 1550 + 50 = 1600 square feet.

The 80% confidence interval for the population mean is between 1500 square feet and 1600 square feet.