Answered: in finding a confidence interval for a…

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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Question

in finding a confidence interval for a random sample of 35 students' GPAs, one interval was (2.65, 3.15) and the other was (2.70, 3.10).

a. One of them is a 95% interval and one is a 90% interval. Which is which, and how do you know?

b. If we used a larger sample size (n=140 instead of n=35, would the 95% interval be wider or narrower than the one reported here?

Choose the correct answer below.

A. The interval (2.70, 3.10) is the 95% interval and (2.65, 3.15) is the 90% interval—a higher level of confidence results in a narrower confidence interval.

B. The interval (2.70, 3.10) is the 95% interval and (2.65, 3.15) is the 90% interval—90% of the data points fall between 2.65 and 3.15.

C. The interval (2.65, 3.15) is the 95% interval and (2.70, 3.10) is the 90% interval—a higher level of confidence results in a wider confidence interval.

D. The interval (2.65, 3.15) is the 95% interval and (2.70, 3.10) is the 90% interval—95% of the data points fall between 2.65 and 3.15.

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Follow-up Question

The 95% interval with n=140 will be narrower than the interval with n=35 because a larger sample size provides a___(smaller, larger)standard error, and this means a ____(smaller,larger)margin of error at the same level of confidence.

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