A stock market analyst notices that in a certain year, the

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

ISBN: 9780073401331 38

Solution for problem 16E Chapter 5.2

Statistics for Engineers and Scientists | 4th Edition

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Problem 16E

A stock market analyst notices that in a certain year, the price of IBM stock increased on 131 out of 252 trading days. Can these data be used to find a 95% confidence interval for the proportion of days that IBM stock increases? Explain

Step-by-Step Solution:

Answer:

Step 1 of 3:

Given, a stock market analyst notices that in a certain year, the price of IBM stock increased in 131 out of 252 trading days.

Here n = 252, x = 131.

Step 2 of 3:

The aim is to find a 95% confidence interval for the proportion of days that IBM stock increases.

Then,

$\widehat{n}=n+4$

= 252+ 4

= 256.

$\widehat{p}=\frac{X+2}{\widehat{n}}$

= $\frac{131+\ 2}{256}$

= 0.5195

A 95% confidence interval for p is given by

$\widehat{p}\ \pm{}{z}_{\alpha{}}\sqrt{\frac{\widehat{p}(1-\widehat{p})}{\widehat{n}}}$ $\$

For a 95% confidence interval: $\frac{\alpha{}}{2}=\frac{0.05}{2}=0.025$

Z - value for 95% confidence interval is ${z}_{0.025}=1.96.$

Then,

$The\ confidence\ interval=0.5195\pm{}1.96\sqrt{\frac{0.5195(1-0.5195)}{256}}$

$\$

$=0.5195\pm{}1.96(0.0312)$

= 0.5195 $\pm{}$ 0.0612

(0.4583, 0.5807)

Step 3 of 3

Chapter 5.2, Problem 16E is Solved

Textbook: Statistics for Engineers and Scientists

Edition: 4

Author: William Navidi

ISBN: 9780073401331

This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The answer to “A stock market analyst notices that in a certain year, the price of IBM stock increased on 131 out of 252 trading days. Can these data be used to find a 95% confidence interval for the proportion of days that IBM stock increases? Explain” is broken down into a number of easy to follow steps, and 44 words. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. Since the solution to 16E from 5.2 chapter was answered, more than 474 students have viewed the full step-by-step answer. This full solution covers the following key subjects: stock, days, IBM, interval, explain. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. The full step-by-step solution to problem: 16E from chapter: 5.2 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM.