Note: For Problem 5 (a), you are asked to find a confidence interval for a population pro- portion. Show your work per the instructions in Problem 1. 5. (a) An accounting firm annually monitors the U.S. Postal Service (USPS). One parameter of interest is the percentage of mail delivered on time. In a sample of 312,000 items mailed between Dec. 10 and Mar. 3 the most difficult delivery season due to bad weather and holidays-the accounting firm determined that 209,103 items were delivered on time. Use this information to make a statement about the likelihood of an item being delivered on time by the USPS. Assuming a confidence level of 90%, the likelihood (in decimal form, rather than %) of an item being delivered on time (when it was mailed between Dec. 10 and Mar. 3) is in the interval (rounded to 3 decimal places) (i) (0.600, 0.740) (ii) (0.657, 0.683) (iii) (0.669, 0.672) (iv) (0.591,0.749) (b) Write down the general formulas for the (1- a)100% confidence interval for the population variance g and the population standard deviation a. For o: For a: (c) Identify each of the mathematical symbols in the formulas you wrote down in part (b) (including the name of any distribution being utilized) and state what conditions about the population must be met in order for these intervals to be valid.
Note: For Problem 5 (a), you are asked to find a confidence interval for a population pro- portion. Show your work per the instructions in Problem 1. 5. (a) An accounting firm annually monitors the U.S. Postal Service (USPS). One parameter of interest is the percentage of mail delivered on time. In a sample of 312,000 items mailed between Dec. 10 and Mar. 3 the most difficult delivery season due to bad weather and holidays-the accounting firm determined that 209,103 items were delivered on time. Use this information to make a statement about the likelihood of an item being delivered on time by the USPS. Assuming a confidence level of 90%, the likelihood (in decimal form, rather than %) of an item being delivered on time (when it was mailed between Dec. 10 and Mar. 3) is in the interval (rounded to 3 decimal places) (i) (0.600, 0.740) (ii) (0.657, 0.683) (iii) (0.669, 0.672) (iv) (0.591,0.749) (b) Write down the general formulas for the (1- a)100% confidence interval for the population variance g and the population standard deviation a. For o: For a: (c) Identify each of the mathematical symbols in the formulas you wrote down in part (b) (including the name of any distribution being utilized) and state what conditions about the population must be met in order for these intervals to be valid.
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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Transcribed Image Text:Note: For Problem 5 (a), you are asked to find a confidence interval for a population pro-
portion. Show your work per the instructions in Problem 1.
5. (a) An accounting firm annually monitors the U.S. Postal Service (USPS). One parameter of interest is
the percentage of mail delivered on time. In a sample of 312,000 items mailed between Dec. 10 and Mar.
3 the most difficult delivery season due to bad weather and holidays the accounting firm determined
that 209,103 items were delivered on time. Use this information to make a statement about the likelihood
of an item being delivered on time by the USPS. Assuming a confidence level of 90%, the likelihood (in
decimal form, rather than %) of an item being delivered on time (when it was mailed between Dec. 10
and Mar. 3) is in the interval (rounded to 3 decimal places)
(i) (0.600, 0.740)
(ii) (0.657, 0.683)
(iii) (0.669, 0.672)
(iv) (0.591,0.749)
(b) Write down the general formulas for the (1– a)100% confidence interval for the population variance
a and the population standard deviation o.
For o?:
For a:
(c) Identify each of the mathematical symbols in the formulas you wrote down in part (b) (including the
name of any distribution being utilized) and state what conditions about the population must be met in
order for these intervals to be valid.
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