Question

The number of square feet per house are normally distributed with a population standard deviation of 197 square feet and an unknown population mean. If a random sample of 25 houses is taken and results in a sample mean of 1820 square feet, find a 99% confidence interval for the population mean.

Answer 1

Answer:

The 99% confidence interval for the population mean is betwen 1718.55 square feet and 1921.45 square feet.

Step-by-step explanation:

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

$\alpha = \frac{1-0.99}{2} = 0.005$

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 $1-0.005 = 0.995$, so $z = 2.575$

Now, find M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

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

$M = 2.575*\frac{197}{\sqrt{25}} = 101.45$

The lower end of the interval is the sample mean subtracted by M. So it is 1820 - 101.45 = 1718.55 square feet

The upper end of the interval is the sample mean added to M. So it is 1820 + 101.45 = 1921.45 square feet.

The 99% confidence interval for the population mean is betwen 1718.55 square feet and 1921.45 square feet.

Answer 2

Answer:

Step-by-step explanation:

(1718.51, 1921.49)