Question

show all 3 relabent steps

mean

standard deviation

distribution

A real-estate company appraised the market value of 25 homes in Jacksonville and found the mean to be $195,125 with a standard deviation of $20,000. The real-estate company also appraised the market value of 33 homes in Orlando and found the mean to be $261,450 with a standard deviation of $27,000. Assume the population standard deviations cannot be assumed equal. a. (5 pts) Find a 99% confidence interval for the true mean difference in market value between Jacksonville and Orlando. b. (2 pts) Is there a significant difference between the market value in Jacksonville and Orlando? Why or why not?

Answer 1

Answer:

Assumptions that need to be met:

In this case, as with the majority of parametric procedures, we need to have that the samples come from normally distributed populations. In this case, we don't have to assume that the population standard deviations are known (which is a more realistic assumption than the case where it is assumed that they are known).

Result Output:

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Ans a)

We need to construct the 1% confidence interval for the difference between the population means Hi U2, for the case that the population standard deviations are not known. The following information has been provided about each of the samples: Sample Mean 1 (X1) = 195125 Sample Standard Deviation 1 (81) = 20000 Sample Size 1 (N1) = 25 Sample Mean 2 (X2) = 261450 Sample Standard Deviation 2 (82) = 27000 Sample Size 2 (N2) = 33 Based on the informationa provided, we assume that the population variances are unequal, so then the number of degrees of freedom is computed as follows: df = (si/nı + sz/n,) 2 = 57.957 (s/ni) 11-1 + (s/n2) n2+1 The critical value for a = 0.99 and df = 57.957 degrees of freedom is te = tı-a/2;n–1 = 0.013. The corresponding confidence interval is computed as shown below: Since we assume that the population variances are unequal, the standard error is computed as follows: se = ni n2 200002 25 + 270002 33 6171 783

Now, we finally compute the confidence interval: CI (X - X2 - te x se, Xi - X2 +te x se) (195125 – 261450 – 0.013 x 6171.783, 195125 – 261450+ 0.013 x 6171.783) = (-66402.688,-66247.312) Therefore, based on the data provided, the 1% confidence interval for the difference between the population means ji – M2 is -66402.688 <Hi – M2 <-66247.312, which indicates that we are 1% confident that the true difference between population means is contained by the interval (-66402.688,-66247.312).

The 99% confidence interval for the true mean difference in market value between Jacksonville and Orlando is ( -66402.688, -66247.312)

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Ans b)

The confidence interval tells you more than just the possible range around the estimate. It also tells you about how stable the estimate is. A stable estimate is one that would be close to the same value if the survey were repeated. An unstable estimate is one that would vary from one sample to another.

There is no significant difference between the market value in Jacksonville and Orlando because the given interval shows a very little difference in Jacksonville and Orlando.

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