You have been hired to work with the nations counterterror a

You have been hired to work with the nation’s counter-terror agency and your initial assignment is to work under one of the top agents, Jack Bauer. However, after a couple days on the job, you hear some startling news. People who are second in command of Jack Bauer’s tactical teams have an incredibly high probability of being shot during the first 20 minutes of an operation (even though you are wearing full body armor and Jack is wearing a t-shirt). Looking back through 6 years of reports, you find that on average, the second in command gets shot 17 minutes into the operation with a standard deviation of 2.2 minutes. This year, the 5 previous agents were shot 21 minutes into the operation. Based on this information, are Jack Bauer’s agents lasting longer before being shot this year as opposed to the previous 6 years? Use a level of significance of 0.05.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   17  
Ha:    u   >   17  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    4          
tcrit =    +   2.131846786      
              
Getting the test statistic, as              
              
X = sample mean =    21          
uo = hypothesized mean =    17          
n = sample size =    5          
s = standard deviation =    2.2          
              
Thus, t = (X - uo) * sqrt(n) / s =    4.065578141          
              
Also, the p value is              
              
p =    0.007639203          
              
As t > 2.1318, and P < 0.05, we   REJECT THE NULL HYPOTHESIS.          

Hence, there is significant evidence that Jack Bauer’s agents lasting longer before being shot this year as opposed to the previous 6 years at 0.05 level. [CONCLUSION]