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Method 1: Use the Student's t distribution with d.f. = n - 1. This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method. Method 2: When n 2 30, use the sample standard deviation s as an estimate for o, and then use the standard normal distribution. This method is based on the fact that for large samples, s is a fairly good approximation for o. Also, for large n, the critical values for the Student's t distribution approach those of the standard normal distribution. Consider a random sample of size n = 41, with sample mean x = 45.5 and sample standard deviation s = 6.5. (a) Compute 90%, 95%, and 99% confidence intervals for u using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal. 90% 95% 99% lower limit upper limit (b) Compute 90%, 95%, and 99% confidence intervals for u using Method 2 with the standard normal distribution. Use s as an estimate for o. Round endpoints to two digits after the decimal. 90% 95% 99% lower limit upper limit (c) Compare intervals for the two methods. Would you say that confidence intervals using a Student's t distribution are more conservative in the sense that they tend to be longer than intervals based on the standard normal distribution? O Yes. The respective intervals based on the t distribution are longer. O No. The respective intervals based on the t distribution are shorter. O Yes. The respective intervals based on the t distribution are shorter. O No. The respective intervals based on the t distribution are longer. (d) Now consider a sample size of 81. Compute 90%, 95%, and 99% confidence intervals for u using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal. 90% 95% 99% lower limit upper limit

Method 1: Use the Student's t distribution with d.f. = n - 1. This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method. Method 2: When n 2 30, use the sample standard deviation s as an estimate for o, and then use the standard normal distribution. This method is based on the fact that for large samples, s is a fairly good approximation for o. Also, for large n, the critical values for the Student's t distribution approach those of the standard normal distribution. Consider a random sample of size n = 41, with sample mean x = 45.5 and sample standard deviation s = 6.5. (a) Compute 90%, 95%, and 99% confidence intervals for u using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal. 90% 95% 99% lower limit upper limit (b) Compute 90%, 95%, and 99% confidence intervals for u using Method 2 with the standard normal distribution. Use s as an estimate for o. Round endpoints to two digits after the decimal. 90% 95% 99% lower limit upper limit (c) Compare intervals for the two methods. Would you say that confidence intervals using a Student's t distribution are more conservative in the sense that they tend to be longer than intervals based on the standard normal distribution? O Yes. The respective intervals based on the t distribution are longer. O No. The respective intervals based on the t distribution are shorter. O Yes. The respective intervals based on the t distribution are shorter. O No. The respective intervals based on the t distribution are longer. (d) Now consider a sample size of 81. Compute 90%, 95%, and 99% confidence intervals for u using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal. 90% 95% 99% lower limit upper limit

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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When o is unknown and the sample is of size n > 30, there are two methods for computing confidence intervals for u. Method 1: Use the Student's t distribution with d.f. = n – 1. This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method. Method 2: When n 2 30, use the sample standard deviation s as an estimate for o, and then use the standard normal distribution. This method is based on the fact that for large samples, s is a fairly good approximation for o. Also, for large n, the critical values for the Student's t distribution approach those of the standard normal distribution. Consider a random sample of size n = 41, with sample mean x = 45.5 and sample standard deviation s = 6.5. (a) Compute 90%, 95%, and 99% confidence intervals for u using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal. 90% 95% 99% lower limit upper limit (b) Compute 90%, 95%, and 99% confidence intervals for u using Method 2 with the standard normal distribution. Use s as an estimate for o. Round endpoints to two digits after the decimal. 90% 95% 99% lower limit upper limit (c) Compare intervals for the two methods. Would you say that confidence intervals using a Student's t distribution are more conservative in the sense that they tend to be longer than intervals based on the standard normal distribution? Yes. The respective intervals based on the t distribution are longer. No. The respective intervals based on the t distribution are shorter. Yes. The respective intervals based on the t distribution are shorter. No. The respective intervals based on the t distribution are longer. (d) Now consider a sample size of 81. Compute 90%, 95%, and 99% confidence intervals for u using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal. 90% 95% 99% lower limit upper limit
Transcribed Image Text:When o is unknown and the sample is of size n > 30, there are two methods for computing confidence intervals for u. Method 1: Use the Student's t distribution with d.f. = n – 1. This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method. Method 2: When n 2 30, use the sample standard deviation s as an estimate for o, and then use the standard normal distribution. This method is based on the fact that for large samples, s is a fairly good approximation for o. Also, for large n, the critical values for the Student's t distribution approach those of the standard normal distribution. Consider a random sample of size n = 41, with sample mean x = 45.5 and sample standard deviation s = 6.5. (a) Compute 90%, 95%, and 99% confidence intervals for u using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal. 90% 95% 99% lower limit upper limit (b) Compute 90%, 95%, and 99% confidence intervals for u using Method 2 with the standard normal distribution. Use s as an estimate for o. Round endpoints to two digits after the decimal. 90% 95% 99% lower limit upper limit (c) Compare intervals for the two methods. Would you say that confidence intervals using a Student's t distribution are more conservative in the sense that they tend to be longer than intervals based on the standard normal distribution? Yes. The respective intervals based on the t distribution are longer. No. The respective intervals based on the t distribution are shorter. Yes. The respective intervals based on the t distribution are shorter. No. The respective intervals based on the t distribution are longer. (d) Now consider a sample size of 81. Compute 90%, 95%, and 99% confidence intervals for u using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal. 90% 95% 99% lower limit upper limit
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