(a) Would a 90% confidence interval calculated from this same sample have been narrower or wider than the given interval? Explain your reasoning. O The 90% would be wider since the z critical value for 90% is smaller than the z critical value for 95%. O The 90% would be narrower since the z critical value for 90% is larger than the z critical value for 95%. O The 90% would be narrower since the z critical value for 90% is smaller than the z critical value for 95%. O The 90% would be wider since the z critical value for 90% is larger than the z critical value for 95%. O The 90% would be the same since the z critical value for 90% is the same as the z critical value for 95%. (b) Consider the following statement: There is a 95% chance that u is between 7.7 and 9.8. Is this statement correct? Why or why not? O It is not a correct statement. There is a 5% chance that the mean is between these values. O It is a correct statement. There is only a 5% chance that the mean is not between these values. O It is not a correct statement. We are 95% confident in the general procedure for creating the interval, but the mean may or may not be enclosed in this interval. O It is a correct statement. Each interval contains the mean by definition. O It is not a correct statement. Each interval contains the mean by definition. (c) Consider the following statement: We can be highly confident that 95% of all bottles of this type of cough syrup have an alcohol content that is between 7.7 and 9.8. I= this statement correct? Why or why not? O It is not a correct statement. The interval is an estimate for the sample mean, not a boundary for population values. O It is a correct statement. This interval is a great estimate of boundaries for population values. O It is not a correct statement. The interval is an estimate for the sample mean, not a boundary for sample values. O It is not a correct statement. The interval is an estimate for the population mean, not a boundary for population values. O It is a correct statement. This is the definition of a confidence interval. 14°C

(a) Would a 90% confidence interval calculated from this same sample have been narrower or wider than the given interval? Explain your reasoning. O The 90% would be wider since the z critical value for 90% is smaller than the z critical value for 95%. O The 90% would be narrower since the z critical value for 90% is larger than the z critical value for 95%. O The 90% would be narrower since the z critical value for 90% is smaller than the z critical value for 95%. O The 90% would be wider since the z critical value for 90% is larger than the z critical value for 95%. O The 90% would be the same since the z critical value for 90% is the same as the z critical value for 95%. (b) Consider the following statement: There is a 95% chance that u is between 7.7 and 9.8. Is this statement correct? Why or why not? O It is not a correct statement. There is a 5% chance that the mean is between these values. O It is a correct statement. There is only a 5% chance that the mean is not between these values. O It is not a correct statement. We are 95% confident in the general procedure for creating the interval, but the mean may or may not be enclosed in this interval. O It is a correct statement. Each interval contains the mean by definition. O It is not a correct statement. Each interval contains the mean by definition. (c) Consider the following statement: We can be highly confident that 95% of all bottles of this type of cough syrup have an alcohol content that is between 7.7 and 9.8. I= this statement correct? Why or why not? O It is not a correct statement. The interval is an estimate for the sample mean, not a boundary for population values. O It is a correct statement. This interval is a great estimate of boundaries for population values. O It is not a correct statement. The interval is an estimate for the sample mean, not a boundary for sample values. O It is not a correct statement. The interval is an estimate for the population mean, not a boundary for population values. O It is a correct statement. This is the definition of a confidence interval. 14°C

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

100%

Can someone please explain it to me all of it??!!! ASAP??!!!

Transcribed Image Text:Suppose that a random sample of 50 bottles of a particular brand of cough syrup is selected and the alcohol content of each bottle is determined. Let u denote the average alcohol content for the population of all bottles of the brand under study. Suppose that the resulting 95% confidence interval is (7.7, 9.8). (a) Would a 90% confidence interval calculated from this same sample have been narrower or wider than the given interval? Explain your reasoning. O The 90% would be wider since the z critical value for 90% is smaller than the z critical value for 95%. O The 90% would be narrower since the z critical value for 90% is larger than the z critical value for 95%. O The 90% would be narrower since the z critical value for 90% is smaller than the z critical value for 95%. O The 90% would be wider since the z critical value for 90% is larger than the z critical value for 95%. O The 90% would be the same since the z critical value for 90% is the same as the z critical value for 95%. (b) Consider the following statement: There is a 95% chance that u is between 7.7 and 9.8. Is this statement correct? Why or why not? O It is not a correct statement. There is a 5% chance that the mean is between these values. O It is a correct statement. There is only a 5% chance that the mean is not between these values. O It is not a correct statement. We are 95% confident in the general procedure for creating the interval, but the mean may or may not be enclosed in this interval. O It is a correct statement. Each interval contains the mean by definition. O It is not a correct statement. Each interval contains the mean by definition. (c) Consider the following statement: We can be highly confident that 95% of all bottles of this type of cough syrup have an alcohol content that is between 7.7 and 9.8. Is this statement correct? Why or why not? O It is not a correct statement. The interval is an estimate for the sample mean, not a boundary for population values. O It is a correct statement. This interval is a great estimate of boundaries for population values. O It is not a correct statement. The interval is an estimate for the sample mean, not a boundary for sample values. O It is not a correct statement. The interval is an estimate for the population mean, not a boundary for population values. O It is a correct statement. This is the definition of a confidence interval. 14°C Partly supRy

(c) Consider the following statement: We can be highly confident that 95% of all bottles of this type of cough syrup have an alcohol content that is between 7.7 and 9.8. Is
this statement correct? Why or why not?
O It is not a correct statement. The interval is an estimate for the sample mean, not a boundary for population values.
O It is a correct statement. This interval is a great estimate of boundaries for population values.
O It is not a correct statement. The interval is an estimate for the sample mean, not a boundary for sample values.
O It is not a correct statement. The interval is an estimate for the population mean, not a boundary for population values.
O It is a correct statement. This is the definition of a confidence interval.
(d) Consider the following statement: If the process of selecting a sample of size 50 and then computing the corresponding 95% interval is repeated 100 times, 95 of the
resulting intervals will include µ. Is this statement correct? Why or why not?
O It is not a correct statement. We expect 5 out of the 100 intervals to contain the mean.
O It is a correct statement. Since we are taking the same sample, we expect all intervals to contain the mean.
O It is not a correct statement. We expect 95 out of 100 intervals will contain the mean, but we don't know this to be true.
O It is not a correct statement. 90 out of the 100 intervals will contain the mean.
O It is a correct statement. This is guaranteed by the definition of confidence interval.
Need Help?
Read It

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here