A professional employee in a large corporation receives an a

A professional employee in a large corporation receives an average or mu = 38.9 e-mans per day. Most of these e-mails are from other employees in the company. Because of the large number of e-mails, employees find themselves distracted and are unable to concentrate when they return to their tasks. In an effort to reduce distraction caused by such interruptions, one company established a priority list that all employees were to use before sending an e-mail. One month after the new priority list was put into place, a random sample of 31 employees showed that they were receiving an average of x = 30.1 e-mails per day. The computer server through which the e-mails are routed showed that alpha = 19.4. Has the new policy had any effect? Use a 10% level of significance to test the claim that there has been a change (either way) in the average number of e-mails received per day per employee. Are the data statistically significant at level alpha? Based on your answers, will you reject or fail to reject the null hypothesis?

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   38.9  
Ha:    u   =/   38.9  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical z, as alpha =    0.1   ,      
alpha/2 =    0.05          
zcrit =    +/-   1.644853627      
              
Getting the test statistic, as              
              
X = sample mean =    30.1          
uo = hypothesized mean =    38.9          
n = sample size =    31          
s = standard deviation =    19.4          
              
Thus, z = (X - uo) * sqrt(n) / s =    -2.525583835          
              
Also, the p value is              
              
p =    0.011550622          
              
As P < 0.10, we reject Ho.

Thus,

OPTION A: The P value is less than the level of significance so the data are statistically significant. [ANSWER, A]