Question

Stellar, Inc. and Zytec, Inc. are two fabricating shops that compete with each other for business. Stellar an established company has been around for more than 20 years and consequently their equipment is somewhat dated. Zytec is a relatively new company and uses cutting edge equipment. Stellar employs 15 mechanics each at $25 per hour, 3 electricians each making $31 per hour, and 17 welders each making $27 per hour. Zytec on the other hand employs 12 mechanics each at $23 per hour, 5 electricians each making $29 per hour, and 21 welders each making $29 per hour. Is the labor cost between these companies significantly different at the .05 level?

Answer 1

Two companies Stellar and Zytec employ mechanic, electricians and welders for their production firm. Stellar is an old company and Zytec is a new company.  

Stellar employs 15 mechanics each at $25 per hour, 3 electricians each making $31 per hour, and 17 welders each making $27 per hour. Zytec on the other hand employs 12 mechanics each at $23 per hour, 5 electricians each making $29 per hour, and 21 welders each making $29 per hour.

To understand whether the labor cost between these companies significantly different at .05 level, we have to test the hypothesis stating null hypothesis whether the labor cost is equal or same against the labor cost is different between these companies.

Considering these two companies, let us take stellar labor costs as X1 ($25,$31,$27) and Zytec as X2 ($23,$29,$29) samples.

So, mean X1= (1/3)(25+31+27)= $27.66 per hour

mean X2= $27 per hour

variance of X1= (1/3)[(25-27.66)^2+(31-27.66)^2+(27-27.66)^2]= 6.22

Variance of X2= 8

Now, in order to test the hypothesis we have to consider t test as the sample size is less than 30 (n1=3, n2=3). Degree of freedom is (n1+n2-2)=4. At 0.05 level of significance t statistic value t(0.025,4)= 2.776. Here, 0.25 because its a two tail t test.

Now, t statistic value= (mean X1-mean X2)/Sp[(1/n1+1/n2)^1/2]= 0.66/1.7556= 0.37

where Sp= {[(n1-1)variance X1+(n2-1)variance x2]/[n1+n2-2]}^1/2= 2.66

Since, t statistic value (0.37) is less than the t critical value (2.776) we reject the null hypothesis that the labor cost is same or equal between the companies.

So, we conclude here that the labor cost between the companies is different at 0.05 laevel of significance.