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2. Repeat Problem 1, however, this time, follow the practice of our textbook which advises the use the of the t-distribution (with df = n- 1) even for large sample confidence intervals for means, if o is unknown (this is a safer practice in terms of covering our confidence; that said, as n increases, the difference between the t-distribution and 2-distribution becomes increasingly negligible; I usually only have you use the t-distribution when a is unknown AND the sample size is small). Here, we have an opportunity (see Part (d) below) to see some consequences (up to two decimal places) of using the t-distribution in place of the z-distribution for n = 90, for a few different confidence levels. Recall from Problem 1 that we have a random sample of 90 observations produced a sample mean of of 7 = 25.9 and a sample standard deviation of s = 2.7. For Parts (a), (b), (c), follow the same instructions for showing your work as provided in Problem 1. (a) The 90% confidence interval for the population mean u is (1) (25.43, 26.37) (ii) (24.29, 27.51) (ii) (2.31, 3.00) (iv) (24.98, 26.82) (b) The 95% confidence interval for the population mean u is (1) (25.33, 26.47) (ii) (24.20, 27.60) (iii) (2.22, 3.18) (iv) (23.99, 27.19) (c) The 99% confidence interval for the population mean u is (i) (25.15, 26.65) (ii) (23.99, 27.81) (iii) (2.01,3.39) (iv) (23.78, 27.40)

2. Repeat Problem 1, however, this time, follow the practice of our textbook which advises the use the of the t-distribution (with df = n- 1) even for large sample confidence intervals for means, if o is unknown (this is a safer practice in terms of covering our confidence; that said, as n increases, the difference between the t-distribution and 2-distribution becomes increasingly negligible; I usually only have you use the t-distribution when a is unknown AND the sample size is small). Here, we have an opportunity (see Part (d) below) to see some consequences (up to two decimal places) of using the t-distribution in place of the z-distribution for n = 90, for a few different confidence levels. Recall from Problem 1 that we have a random sample of 90 observations produced a sample mean of of 7 = 25.9 and a sample standard deviation of s = 2.7. For Parts (a), (b), (c), follow the same instructions for showing your work as provided in Problem 1. (a) The 90% confidence interval for the population mean u is (1) (25.43, 26.37) (ii) (24.29, 27.51) (ii) (2.31, 3.00) (iv) (24.98, 26.82) (b) The 95% confidence interval for the population mean u is (1) (25.33, 26.47) (ii) (24.20, 27.60) (iii) (2.22, 3.18) (iv) (23.99, 27.19) (c) The 99% confidence interval for the population mean u is (i) (25.15, 26.65) (ii) (23.99, 27.81) (iii) (2.01,3.39) (iv) (23.78, 27.40)

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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2. Repeat Problem 1, however, this time, follow the practice of our textbook which advises the use the of the t-distribution (with df = n- 1) even for large sample confidence intervals for means, if o is unknown (this is a safer practice in terms of covering our confidence; that said, as n increases, the difference between the t-distribution and z-distribution becomes increasingly negligible; I usually only have you use the t-distribution when a is unknown AND the sample size is small). Here, we have an opportunity (see Part (d) below) to see some consequences (up to two decimal places) of using the t-distribution in place of the z-distribution for n = 90, for a few different confidence levels. Recall from Problem 1 that we have a random sample of 90 observations produced a sample mean of of 7 = 25.9 and a sample standard deviation of s = 2.7. For Parts (a), (b), (c), follow the same instructions for showing your work as provided in Problem 1. (a) The 90% confidence interval for the population mean u is (1) (25.43, 26.37) (ii) (24.29, 27.51) (iii) (2.31, 3.09) (iv) (24.98, 26.82) (b) The 95% confidence interval for the population mean a is (i) (25.33, 26.47) (ii) (24.20, 27.60) (iii) (2.22, 3.18) (iv) (23.99, 27.19) (c) The 99% confidence interval for the population mean a is (i) (25.15, 26.65) (ii) (23.99, 27.81) (iii) (2.01, 3.39) (iv) (23.78, 27.40) (d) Compare your answers from Problem 1 and Problem 2. Explain any discrepancies (in particular, în your explanation, point out a difference in the characteristic/shape of the the t-distribution from the z-distribution which cause any discrepancy).
Transcribed Image Text:2. Repeat Problem 1, however, this time, follow the practice of our textbook which advises the use the of the t-distribution (with df = n- 1) even for large sample confidence intervals for means, if o is unknown (this is a safer practice in terms of covering our confidence; that said, as n increases, the difference between the t-distribution and z-distribution becomes increasingly negligible; I usually only have you use the t-distribution when a is unknown AND the sample size is small). Here, we have an opportunity (see Part (d) below) to see some consequences (up to two decimal places) of using the t-distribution in place of the z-distribution for n = 90, for a few different confidence levels. Recall from Problem 1 that we have a random sample of 90 observations produced a sample mean of of 7 = 25.9 and a sample standard deviation of s = 2.7. For Parts (a), (b), (c), follow the same instructions for showing your work as provided in Problem 1. (a) The 90% confidence interval for the population mean u is (1) (25.43, 26.37) (ii) (24.29, 27.51) (iii) (2.31, 3.09) (iv) (24.98, 26.82) (b) The 95% confidence interval for the population mean a is (i) (25.33, 26.47) (ii) (24.20, 27.60) (iii) (2.22, 3.18) (iv) (23.99, 27.19) (c) The 99% confidence interval for the population mean a is (i) (25.15, 26.65) (ii) (23.99, 27.81) (iii) (2.01, 3.39) (iv) (23.78, 27.40) (d) Compare your answers from Problem 1 and Problem 2. Explain any discrepancies (in particular, în your explanation, point out a difference in the characteristic/shape of the the t-distribution from the z-distribution which cause any discrepancy).
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