Answered: Based on the information from the U.S…

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

Based on the information from the U.S census bureau the mean travel time to work in minutes for all workers 16 years old and older was 27.5 minutes. A large company with offices in several states randomly sample 85 of its workers to ascertain their commuting times. The sample mean was 23.6 minutes,and the population standard deviation is 5.41 minutes. At the 0.05 level of signifance can it be concluded that the mean commuting time is less for this particular company

Expert Solution

Step 1

Given:

$\begin{array}{rcl} \bar{x} & = & 23.6 \\ σ & = & 5.41 \\ n & = & 85 \\ μ & = & 27.5 \end{array}$

Hypothesis:

$\begin{array}{rcl} Null hypothesis : H_{0} : μ & = & 27.5 \\ Alternate hypothesis : H_{1} : μ & < & 27.5 \end{array}$

The test statistic is obtained as below:

$\begin{array}{rcl} z & = & \frac{sample statistic - Null parameter}{SE} \\ = & \frac{\bar{x} - μ}{\frac{σ}{\sqrt{n}}} \\ = & \frac{23.6 - 27.5}{\frac{5.41}{\sqrt{85}}} \\ = & \frac{- 3.9}{0.5868} \\ = & - 6.6462 \end{array}$

Thus, the test statistic is -6.6462.

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