Mathematics, 11.12.2019 05:31 MadisonUpky9652

The realtor and her clients do not know the average home sale price for all of guelph (500 was actually just a guess). however, they calculate that average sale price for their 15 listings is 400.
(a) given that the standard deviation of sale prices is known to be 80, calculate a 99 percent confidence interval for the average sale price in guelph.
(b) given that the standard deviation of sale prices is unknown but estimated to be 80, calculate a 99 percent confidence interval for the average sale price in guelph.

Answers: 3

Show answers

Answers

Answer from: durham953

a) The 99% confidence interval would be given by (346.708;453.292)

b) The 99% confidence interval would be given by (338.445;461.555)

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=400$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=80$ represent the population standard deviation

n=15 represent the sample size

2) Part a

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that $z_{\alpha/2}=2.58$

Now we have everything in order to replace into formula (1):

$400-2.58\frac{80}{\sqrt{15}}=346.708$

$400+2.58\frac{80}{\sqrt{15}}=453.292$

So on this case the 99% confidence interval would be given by (346.708;453.292)

3) Part b

For this case we don't know the population deviation so we need to use the t distribution instead the normal standard distribution.

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

We need to find the degrees of freedom first df=n-1=15-1=14

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,14)".And we see that $t_{\alpha/2}=2.98$

Now we have everything in order to replace into formula (1):

$400-2.98\frac{80}{\sqrt{15}}=338.445$

$400+2.98\frac{80}{\sqrt{15}}=461.555$

So on this case the 99% confidence interval would be given by (338.445;461.555)

Answer from: Quest

What is your question?

Answer from: Quest

im here

step-by-step explanation:

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 21:50, jules8022

Match each whole number with a rational, exponential expression 3 square root 27^2find the domain and range of the exponential function h(x)=125^x. explain your findings. as x decreases does h increase or decrease? explain. as x increases does h increase or decrease? explain.

Answers: 3

continue

Mathematics, 21.06.2019 23:00, moncho6222

72 the length of a side of a triangle is 36. a line parallel to that side divides the triangle into two parts of equal area. find the length of the segment determined by the points of intersection between the line and the other two sides of the triangle.

Answers: 1

continue

Mathematics, 21.06.2019 23:00, utjfkdndidndldn62121

Why is it so easy to buy on impulse and overspend with a credit card? what could you do to counteract this tendency?

Answers: 1

continue

Mathematics, 21.06.2019 23:30, sandy2597

Find measure angle 1 and measure angle 3 in the kite the diagram is not drawn on the scale

Answers: 1

continue

You know the right answer?

The realtor and her clients do not know the average home sale price for all of guelph (500 was actua...