The housing market has recovered slowly from the economic crisis of 2008. Recently, in one large community, realtors randomly sampled 42 bids from potential buyers to estimate the average loss in home value. The sample showed the average loss was$9035 with a standard deviation of $3000. Suppose a 95% confidence interval to estimate the average loss in home value is found. Complete parts a through c below. a) Suppose the standard deviation of the losses had been $9000 instead of $3000. What would the larger standard deviation do to the width of the confidence interval (assuming the same level of confidence)? A. A larger standard deviation would not change the width of the confidence interval. B. A larger standard deviation decreases the width of the confidence interval. C. A larger standard deviation increases the width of the confidence interval. D. Depending on the level of confidence a larger standard deviation might increase or decrease the width of the confidence interval. Part 2 b) A classmate suggests that the margin of error in the interval could be reduced if the confidence level were changed to 90% instead of 95%. Do you agree with this statement? Why or why not? A. No, because the width of the confidence interval does not depend on the confidence level. B. No, because a lower confidence level might make the confidence interval narrower for some confidence intervals but it might make it wider instead. C. Yes, because a lower confidence level can make the confidence interval narrower. D. No, because a lower confidence level would make the confidence interval wider. Part 3 c) Instead of changing the level of confidence, would it be more statistically appropriate to draw a bigger sample? A. A larger sample size would reduce the standard error of the mean and make the confidence interval narrower. It would be more statistically appropriate. B. A larger sample size would increase the standard error of the mean and make the confidence interval wider. It would not be more statistically appropriate. C. A larger sample size would only make the confidence interval narrower if the level of confidence is 95% or less. D. A larger sample size would only reduce the standard error up to n=30.A sample size larger than 30 would not change the size of the standard error. It would not be more statistically appropriate.

The housing market has recovered slowly from the economic crisis of 2008. Recently, in one large community, realtors randomly sampled 42 bids from potential buyers to estimate the average loss in home value. The sample showed the average loss was$9035 with a standard deviation of $3000. Suppose a 95% confidence interval to estimate the average loss in home value is found. Complete parts a through c below. a) Suppose the standard deviation of the losses had been $9000 instead of $3000. What would the larger standard deviation do to the width of the confidence interval (assuming the same level of confidence)? A. A larger standard deviation would not change the width of the confidence interval. B. A larger standard deviation decreases the width of the confidence interval. C. A larger standard deviation increases the width of the confidence interval. D. Depending on the level of confidence a larger standard deviation might increase or decrease the width of the confidence interval. Part 2 b) A classmate suggests that the margin of error in the interval could be reduced if the confidence level were changed to 90% instead of 95%. Do you agree with this statement? Why or why not? A. No, because the width of the confidence interval does not depend on the confidence level. B. No, because a lower confidence level might make the confidence interval narrower for some confidence intervals but it might make it wider instead. C. Yes, because a lower confidence level can make the confidence interval narrower. D. No, because a lower confidence level would make the confidence interval wider. Part 3 c) Instead of changing the level of confidence, would it be more statistically appropriate to draw a bigger sample? A. A larger sample size would reduce the standard error of the mean and make the confidence interval narrower. It would be more statistically appropriate. B. A larger sample size would increase the standard error of the mean and make the confidence interval wider. It would not be more statistically appropriate. C. A larger sample size would only make the confidence interval narrower if the level of confidence is 95% or less. D. A larger sample size would only reduce the standard error up to n=30.A sample size larger than 30 would not change the size of the standard error. It would not be more statistically appropriate.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Part 2

b) A classmate suggests that the margin of error in the interval could be reduced if the confidence level were changed to 90% instead of 95%. Do you agree with this statement? Why or why not?

No, because the width of the confidence interval does not depend on the confidence level.

No, because a lower confidence level might make the confidence interval narrower for some confidence intervals but it might make it wider instead.

Yes, because a lower confidence level can make the confidence interval narrower.

No, because a lower confidence level would make the confidence interval wider.

Part 3

c) Instead of changing the level of confidence, would it be more statistically appropriate to draw a bigger sample?

A larger sample size would reduce the standard error of the mean and make the confidence interval narrower. It would be more statistically appropriate.

A larger sample size would increase the standard error of the mean and make the confidence interval wider. It would not be more statistically appropriate.

A larger sample size would only make the confidence interval narrower if the level of confidence is 95% or less.

A larger sample size would only reduce the standard error up to n=30.A sample size larger than 30 would not change the size of the standard error. It would not be more statistically appropriate.

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