A drapery store manager was interested in determining whethe

A drapery store manager was interested in determining whether a new employee can install vertical blinds faster than an employee who has been with the company for two years. The manager takes independent samples of 10 vertical blind installations of each of the two employees and computes the following information.

New Employee

Veteran Employee

Sample Size

10

10

Sample Mean

22.2 min

24.8 min

Standard Deviation

0.90 min

0.75 min

A drapery store manager was interested in determining whether a new employee can install vertical blinds faster than an employee who has been with the company for two years. The manager takes independent samples of 10 vertical blind installations of each of the two employees and computes the following information.

New Employee

Veteran Employee

Sample Size

10

10

Sample Mean

22.2 min

24.8 min

Standard Deviation

0.90 min

0.75 min

Using the null and alternate hypothesis:
H0:mu1-mu2=0 vs. Ha:mu1-mu2<0
Calculate the value of the test statistic

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   >=   0  
Ha:   u1 - u2   <   0  
At level of significance =    0.05          
As we can see, this is a    left   tailed test.      
Calculating the means of each group,              
              
X1 =    22.2          
X2 =    24.8          
              
Calculating the standard deviations of each group,              
              
s1 =    0.9          
s2 =    0.75          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    10          
n2 = sample size of group 2 =    10          
Thus, df = n1 + n2 - 2 =    18          
Also, sD =    0.370472671          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    -7.018061528 [ANSWER, TEST STATISTIC]