Problem 4. A large company is conducting a study on commuting distance among itsemployees. A sample of 35 employees in the New York office has a mean of 370 milesper month. A sample of 40 employees in the Chicago office has a mean of 380 miles permonth. The population standard deviations for the New York and Chicago employees are30 and 26 miles, respectively. Is there a difference in the mean travel distance betweenthe two locations?a. Setup the appropriate null and alternative hypotheses.b. Construct the relevant test statistic.c. Test the hypotheses at the 0.05 significance level and state your conclusion.

Answered: Problem 4. A large company is…

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

Problem 4. A large company is conducting a study on commuting distance among its
employees. A sample of 35 employees in the New York office has a mean of 370 miles
per month. A sample of 40 employees in the Chicago office has a mean of 380 miles per
month. The population standard deviations for the New York and Chicago employees are
30 and 26 miles, respectively. Is there a difference in the mean travel distance between
the two locations?
a. Setup the appropriate null and alternative hypotheses.
b. Construct the relevant test statistic.
c. Test the hypotheses at the 0.05 significance level and state your conclusion.

Expert Solution

Step 1

Solution:

Given information:

$n_{1} = 35 S a m p l e s i z e o f N e w Y o r k e m p l o y e e s n_{2} = 40 S a m p l e s i z e o f C h i c a g o e m p l o y e e s x_{1} = 370 S a m p l e m e a n o f N e w Y o r k e m p l o y e e s x_{2} = 380 S a m p l e m e a n o f C h i c a g o e m p l o y e e s σ_{1} = 30 P o p u l a t i o n s \tan d a r d d e v i a t i o n o f N e w Y o r k e m p l o y e e s σ_{2} = 26 P o p u l a t i o n s \tan d a r d d e v i a t i o n o f C h i c a g o e m p l o y e e s$