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Stels [109]
3 years ago
10

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.
Mathematics
1 answer:
strojnjashka [21]3 years ago
4 0

Answer:

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)    

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marin [14]
1. Take your 13.75 and 5 1/2 and put it into a dividing table 
           _______
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                              you need to get your decimal out of deviser (5.5) will now be (55) because you moved the decimal over there you also need to move the decimal that is on the inside to and it will be (137.5)

2. When you divide you would get 2.5 

3. Now you would know how much the tree grew over the 5 1/2 years.

ANSWER:  2.5m a year!

Hope this helped! 

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How do you solve 5(N+4)/3 = N-8
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Answer:

n=-22

Step-by-step explanation:

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  • For a continuous probability distribution, the mean s given by, E(x) = \int x_if(x_i), where f(x) is the probability density function.
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