Question

In one​ community, a random sample of

2727

foreclosed homes sold for an average of

​$440 comma 396440,396

with a standard deviation of

​$196 comma 981196,981.

​a)	What assumptions and conditions must be checked before finding a confidence interval for the​ mean? How would you check​ them?
​b)	Find a 9999​% confidence interval for the mean value per home.
​c)	Interpret this interval and explain what 9999​% confidence means.
​d)	Suppose​ nationally, the average foreclosed home sold for ​$389 comma 000389,000. Do you think the average sale price in the sampled community differs significantly from the national​ average? Explain.

Answer 1

a)

The assumption that must be checked are:

Independence, randomization and normality of data

Also, normality of data can be checked using Kolmogrov-smirnov test.

b)

We know that the 99% confidence interval for population mean is given by:

c)

We can say with 99% confidence that the population mean lies in the interval .

d)

The null and alternate hypothesis are:

H0:

Ha:

Since the value 389000 lies in the 99% confidence interval for population mean, so we do not have sufficient evidence to reject H0 at 1% level of significance.

So, we say that the average sale price in the sampled community does not differ significantly from the national​ average.