Suppose that a random sample of 50 cans of a particular brand of fruit juice is selected, and the amount of juice (in ounces) in each of the cans is determined. Let ? denote the mean amount of juice for the population of all cans of this brand. Suppose that this sample of 50 results in a 95% confidence interval for ? of (7.4, 8.8). (a) Would a 90% confidence interval have been narrower or wider than the given interval? Explain your answer. A 90% confidence interval would have been narrower because the t critical value for 90% confidence is smaller than the t critical value for 95% confidence for the same sample size.A 90% confidence interval would have been narrower because the t critical value for 90% confidence is larger than the t critical value for 95% confidence for the same sample size. A 90% confidence interval would have been wider because the t critical value for 90% confidence is smaller than the t critical value for 95% confidence for the same sample size.A 90% confidence interval would have been wider because the t critical value for 90% confidence is larger than the t critical value for 95% confidence for the same sample size. (b) Consider the following statement: There is a 95% chance that ? is between 7.4 and 8.8. Is this statement correct? Why or why not? The statement is correct. The population mean, ?, is not a constant, and therefore, we can talk about the probability that it falls within a certain interval.The statement is correct. The population mean, ?, is a constant, and therefore, we can talk about the probability that it falls within a certain interval. The statement is not correct. The population mean, ?, is not a constant, and therefore, we cannot talk about the probability that it falls within a certain interval.The statement is not correct. The population mean, ?, is a constant, and therefore, we cannot talk about the probability that it falls within a certain interval. (c) Consider the following statement. If the process of selecting a random sample of size 50 and then calculating the corresponding 95% confidence interval is repeated 100 times, exactly 95 of the resulting intervals will include ?. Is this statement correct? Why or why not? The statement is correct. Since it is repeated more than 30 times, we can say that in 100 such samples, exactly 95 will result in confidence intervals that contain ?.The statement is correct. Since the sample size is large, we can say that in 100 such samples, exactly 95 will result in confidence intervals that contain ?. The statement is not correct. We can only say that on average 95 out of every 100 samples will result in confidence intervals that will contain ?.The statement is not correct. We can only say that on average 5 out of every 100 samples will result in confidence intervals that will contain ?.

Suppose that a random sample of 50 cans of a particular brand of fruit juice is selected, and the amount of juice (in ounces) in each of the cans is determined. Let ? denote the mean amount of juice for the population of all cans of this brand. Suppose that this sample of 50 results in a 95% confidence interval for ? of (7.4, 8.8). (a) Would a 90% confidence interval have been narrower or wider than the given interval? Explain your answer. A 90% confidence interval would have been narrower because the t critical value for 90% confidence is smaller than the t critical value for 95% confidence for the same sample size.A 90% confidence interval would have been narrower because the t critical value for 90% confidence is larger than the t critical value for 95% confidence for the same sample size. A 90% confidence interval would have been wider because the t critical value for 90% confidence is smaller than the t critical value for 95% confidence for the same sample size.A 90% confidence interval would have been wider because the t critical value for 90% confidence is larger than the t critical value for 95% confidence for the same sample size. (b) Consider the following statement: There is a 95% chance that ? is between 7.4 and 8.8. Is this statement correct? Why or why not? The statement is correct. The population mean, ?, is not a constant, and therefore, we can talk about the probability that it falls within a certain interval.The statement is correct. The population mean, ?, is a constant, and therefore, we can talk about the probability that it falls within a certain interval. The statement is not correct. The population mean, ?, is not a constant, and therefore, we cannot talk about the probability that it falls within a certain interval.The statement is not correct. The population mean, ?, is a constant, and therefore, we cannot talk about the probability that it falls within a certain interval. (c) Consider the following statement. If the process of selecting a random sample of size 50 and then calculating the corresponding 95% confidence interval is repeated 100 times, exactly 95 of the resulting intervals will include ?. Is this statement correct? Why or why not? The statement is correct. Since it is repeated more than 30 times, we can say that in 100 such samples, exactly 95 will result in confidence intervals that contain ?.The statement is correct. Since the sample size is large, we can say that in 100 such samples, exactly 95 will result in confidence intervals that contain ?. The statement is not correct. We can only say that on average 95 out of every 100 samples will result in confidence intervals that will contain ?.The statement is not correct. We can only say that on average 5 out of every 100 samples will result in confidence intervals that will contain ?.

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

Concept explainers

Question

(7.4, 8.8).

(a)

Would a 90% confidence interval have been narrower or wider than the given interval? Explain your answer.

A 90% confidence interval would have been narrower because the t critical value for 90% confidence is smaller than the t critical value for 95% confidence for the same sample size.A 90% confidence interval would have been narrower because the t critical value for 90% confidence is larger than the t critical value for 95% confidence for the same sample size. A 90% confidence interval would have been wider because the t critical value for 90% confidence is smaller than the t critical value for 95% confidence for the same sample size.A 90% confidence interval would have been wider because the t critical value for 90% confidence is larger than the t critical value for 95% confidence for the same sample size.

(b)

Consider the following statement: There is a 95% chance that ? is between 7.4 and 8.8. Is this statement correct? Why or why not?

The statement is correct. The population mean, ?, is not a constant, and therefore, we can talk about the probability that it falls within a certain interval.The statement is correct. The population mean, ?, is a constant, and therefore, we can talk about the probability that it falls within a certain interval. The statement is not correct. The population mean, ?, is not a constant, and therefore, we cannot talk about the probability that it falls within a certain interval.The statement is not correct. The population mean, ?, is a constant, and therefore, we cannot talk about the probability that it falls within a certain interval.

(c)

Consider the following statement.

If the process of selecting a random sample of size 50 and then calculating the corresponding 95% confidence interval is repeated 100 times, exactly 95 of the resulting intervals will include ?.

Is this statement correct? Why or why not?

The statement is correct. Since it is repeated more than 30 times, we can say that in 100 such samples, exactly 95 will result in confidence intervals that contain ?.The statement is correct. Since the sample size is large, we can say that in 100 such samples, exactly 95 will result in confidence intervals that contain ?. The statement is not correct. We can only say that on average 95 out of every 100 samples will result in confidence intervals that will contain ?.The statement is not correct. We can only say that on average 5 out of every 100 samples will result in confidence intervals that will contain ?.

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.