Answered: In a sample of 225 college seniors, 182…

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 a sample of 225 college seniors, 182 responded positively when asked if they have spring fever. Based upon this, compute a 90% confidence interval for the proportion of all college seniors who have spring fever. Then find the lower limit and upper limit of the 90%
confidence interval.

Carry your intermediate computations to at least three decimal places. Round your answers to two decimal places.

Lower limit:
Upper limit:

Expert Solution

Step 1

It is given that, in a sample of 225 college seniors, 182 responded positively when asked if they have spring fever.

x=182

n=225

(p̂) = x/n= 182/225 = 0.809

The 90% confidence interval can be calculated as:

$C I = (\hat{p} \pm Z_{α / 2} \sqrt{\frac{\hat{p} (1 - \hat{p})}{n}})$

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