In one community, a random sample of 26 foreclosed homes sold for an average of $443 comma 555 with a standard deviation of $195 comma 381. a) What assumptions and conditions must be checked before finding a confidence interval for the mean? How would you check them? b) Find a 95% confidence interval for the mean value per home. c) Interpret this interval and explain what 95% confidence means. d) Suppose nationally, the average foreclosed home sold for $300 comma 000. Do you think the average sale price in the sampled community differs significantly from the national average? Explain. c

i) a) Normality : We assume that the data follows approximately a normal distribution

ii) Random sample: The data comes from a random sample

iii) The sample size represent <10% of the population size

We assume that all the conditions are satisfied for this case.

b)    

So on this case the 95% confidence interval would be given by (364621.22;522488.775)    

c) We are confident at 95% that the true mean of foreclosed homes sold's are between (364621.22;522488.775)    

d) Since the lower value for the 95% confidence interval is higher than 300000 we can conclude that yes differes significantly and the true mean is different from 300000 at 5% of significance.

Step-by-step explanation:

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".

represent the sample mean

population mean (variable of interest)

s=195381 represent the sample standard deviation

n=26 represent the sample size  

Part a

We need some conditions:

a) Normality : We assume that the data follows approximately a normal distribution

b) Random sample: The data comes from a random sample

c) The sample size represent <10% of the population size

We assume that all the conditions are satisfied for this case.

Part b

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

  (1)

In order to calculate the critical value we need to find first the degrees of freedom, given by:

Since the Confidence is 0.95 or 95%, the value of and , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,25)".And we see that

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

So on this case the 95% confidence interval would be given by (364621.22;522488.775)    

Part c

We are confident at 95% that the true mean of foreclosed homes sold's are between (364621.22;522488.775)    

Part d

Since the lower value for the 95% confidence interval is higher than 300000 we can conclude that yes differes significantly and the true mean is different from 300000 at 5% of significance.

its a straight line parallel to the time axis

a

step-by-step explanation: