Mathematics: 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: the answer is bstep-by-step explanation:...

The number of square feet per house is normally

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21.01.2022

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

$\alpha = \frac{1-0.8}{2} = 0.1$

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

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

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

$M = 1.282*\frac{156}{\sqrt{16}} = 50$

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.

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