One year, a large number of foreclosed homes in the Washington, DC, metro area w

Question

One year, a large number of foreclosed homes in the Washington, DC, metro area were sold. In one community, a sample of 30 foreclosed homes sold for an average of $443,655 with a standard deviation of $196,120. Complete parts (a) through (c) below. (a) Suppose the standard deviation of the values was $300,000 instead of the $196,120 used for a confidence interval. What would the larger standard deviation do to the width of the confidence interval (assuming the same level of confidence)? O A. A larger standard deviation decreases the standard emor and will decrease the width of the confidence interval. O B. A larger standard deviation decreases the standard error and will increase the width of the confidence interval. O C. Alarger standard deviation increases the standard error and will increase the width of the confidence interval O D. A larger standard deviation increases the standard error and will decrease the width of the confidence interval. b Your classmate suggests that the margin of error in the interval could be reduce if the confidence inter ere changed to 90% ns ad of % Do you agree with his state t? why or not? O A. The margin or error is reduced when the level of confidence is reduced. This is because a lower level of confidence captures a larger percentage of possible sample means. O B. The margin or error is increased when the level of confidence is reduced. This is because a lower level of confidence captures a larger percentage of possible sample means. O C. The margin or error is reduced when the level of confidence is reduced. This is because a lower level of confidence captures a smaller percentage of possible sample means. D he mar n or error is increased when the level o confidence is reduced. hs s because a lower leve o confidence captures a smaller percenta e o possible a means (c) Instead of changing the level of confidence, would it be more statistically appropriate to draw a bigger sample? A. A larger sample size increases the standard error, and thus increase the margin of error. O B. A larger sample size reduces the standard error, and thus decrease the margin of error. O C. A larger sample size reduces the standard error, and thus increase the margin of error O D. A larger sample size increases the standard error, and thus decrease the margin of error.

Explanation / Answer

Ans:

a)larger standard deviation will increase the standard error and will increase the width of the confidence interval.

Confidence interval=point estimate+/-multiplier*standard error

Option C is correct.

b)z multiplier for 95% is 1.96

z multiplier for 90% is 1.645

As,the confidence level reduces,multiplier value reduces.

So,it will give lesser margin of error,if we change the confidence interval from 95% to 90%.

Option C is correct.

c)Larger sample size reduces the standard error and So, decrease the margin of error.

Standard error=std dev/sqrt(n)

Option B is correct.

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