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18 (c) Notice that for =90% of the samples, the 95% confidence interval contains the population mean. Choose the 20 correct statement. O When constructing 95% confidence intervals for 20 samples of the same size from the population, exactly 95% of the samples will contain the population mean. O When constructing 95% confidence intervals for 20 samples of the same size from the population, at most 95% of the samples will contain the population mean. When constructing 95% confidence intervals for 20 samples of the same size from the population, it is possible that more or fewer than 95% of the samples will contain the population mean. (d) Choose ALL that are true. If there were a Sample 21 of size n=24 taken from the same population as Sample 11, then the 95% confidence interval for Sample 21 would be narrower than the 95% confidence interval for Sample 11. The 80% confidence interval for Sample 11 is narrower than the 95% confidence interval for Sample 11. This is coincidence; when constructing a confidence interval for a sample, there is no relationship between the level of confidence and the width of the interval. From the 95% confidence interval for Sample 11, we cannot say that there is a 95% probability that the population mean is between 87.6 and 92.2. The 80% confidence interval for Sample 11 does not indicate that 80% of the Sample 11 data values are between 88.4 and 91.4. None of the choices above are true

18 (c) Notice that for =90% of the samples, the 95% confidence interval contains the population mean. Choose the 20 correct statement. O When constructing 95% confidence intervals for 20 samples of the same size from the population, exactly 95% of the samples will contain the population mean. O When constructing 95% confidence intervals for 20 samples of the same size from the population, at most 95% of the samples will contain the population mean. When constructing 95% confidence intervals for 20 samples of the same size from the population, it is possible that more or fewer than 95% of the samples will contain the population mean. (d) Choose ALL that are true. If there were a Sample 21 of size n=24 taken from the same population as Sample 11, then the 95% confidence interval for Sample 21 would be narrower than the 95% confidence interval for Sample 11. The 80% confidence interval for Sample 11 is narrower than the 95% confidence interval for Sample 11. This is coincidence; when constructing a confidence interval for a sample, there is no relationship between the level of confidence and the width of the interval. From the 95% confidence interval for Sample 11, we cannot say that there is a 95% probability that the population mean is between 87.6 and 92.2. The 80% confidence interval for Sample 11 does not indicate that 80% of the Sample 11 data values are between 88.4 and 91.4. None of the choices above are true

MATLAB: An Introduction with Applications
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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You have taken a random sample of size n = 12 from a normal population that has a population mean of μ = 90 and a population standard deviation of o=4. Your sample, which is Sample 1 in the table below, has a mean of x=90.8. (In the table, Sample 1 is written "S1", Sample 2 is written "S2", etc.) (a) Based on Sample 1, graph the 80% and 95% confidence intervals for the population mean. Use 1.282 for the critical value for the 80% confidence interval, and use 1.960 for the critical value for the 95% confidence interval. (If necessary, consult a list of formulas.) • Enter the lower and upper limits on the graphs to show each confidence interval. Write your answers with one decimal place. • For the points (and ◆), enter the population mean, μ = 90. 83.0 HHHH 83.0 80% confidence interval 90.0 95.0 ▬▬▬▬▬▬▬▬▬▬▬H X 95.0 83.0 83.0 95% confidence interval 90.0 X 95.0 +++|| 3 95.0
Transcribed Image Text:You have taken a random sample of size n = 12 from a normal population that has a population mean of μ = 90 and a population standard deviation of o=4. Your sample, which is Sample 1 in the table below, has a mean of x=90.8. (In the table, Sample 1 is written "S1", Sample 2 is written "S2", etc.) (a) Based on Sample 1, graph the 80% and 95% confidence intervals for the population mean. Use 1.282 for the critical value for the 80% confidence interval, and use 1.960 for the critical value for the 95% confidence interval. (If necessary, consult a list of formulas.) • Enter the lower and upper limits on the graphs to show each confidence interval. Write your answers with one decimal place. • For the points (and ◆), enter the population mean, μ = 90. 83.0 HHHH 83.0 80% confidence interval 90.0 95.0 ▬▬▬▬▬▬▬▬▬▬▬H X 95.0 83.0 83.0 95% confidence interval 90.0 X 95.0 +++|| 3 95.0
18 (c) Notice that for =90% of the samples, the 95% confidence interval contains the population mean. Choose the 20 correct statement. O When constructing 95% confidence intervals for 20 samples of the same size from the population, exactly 95% of the samples will contain the population mean. O When constructing 95% confidence intervals for 20 samples of the same size from the population, at most 95% of the samples will contain the population mean. When constructing 95% confidence intervals for 20 samples of the same size from the population, it is possible that more or fewer than 95% of the samples will contain the population mean. (d) Choose ALL that are true. ✔ If there were a Sample 21 of size n=24 taken from the same population as Sample 11, then the 95% confidence interval for Sample 21 would be narrower than the 95% confidence interval for Sample 11. ✔ The 80% confidence interval for Sample 11 is narrower than the 95% confidence interval for Sample 11. This is coincidence; when constructing a confidence interval for a sample, there is no relationship between the level of confidence and the width of the interval. ✔ From the 95% confidence interval for Sample 11, we cannot say that there is a 95% probability that the population mean is between 87.6 and 92.2. The 80% confidence interval for Sample 11 does not indicate that 80% of the Sample 11 data values are between 88.4 and 91.4. None of the choices above are true. ?
Transcribed Image Text:18 (c) Notice that for =90% of the samples, the 95% confidence interval contains the population mean. Choose the 20 correct statement. O When constructing 95% confidence intervals for 20 samples of the same size from the population, exactly 95% of the samples will contain the population mean. O When constructing 95% confidence intervals for 20 samples of the same size from the population, at most 95% of the samples will contain the population mean. When constructing 95% confidence intervals for 20 samples of the same size from the population, it is possible that more or fewer than 95% of the samples will contain the population mean. (d) Choose ALL that are true. ✔ If there were a Sample 21 of size n=24 taken from the same population as Sample 11, then the 95% confidence interval for Sample 21 would be narrower than the 95% confidence interval for Sample 11. ✔ The 80% confidence interval for Sample 11 is narrower than the 95% confidence interval for Sample 11. This is coincidence; when constructing a confidence interval for a sample, there is no relationship between the level of confidence and the width of the interval. ✔ From the 95% confidence interval for Sample 11, we cannot say that there is a 95% probability that the population mean is between 87.6 and 92.2. The 80% confidence interval for Sample 11 does not indicate that 80% of the Sample 11 data values are between 88.4 and 91.4. None of the choices above are true. ?
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