Most video games have several difficulty settings from Easy

Most video games have several difficulty settings, from \"Easy\" to \"Hard\" (many of these have very colorful names). A video game designer wants to determine how to structure the difficulty levels for a new game so that the average time it takes the typical player to play through \"Hard\" mode is two hours longer than the average time to play through \"Easy\" mode. A sample (Group 1) of 10 typical players took an average of 6 hours to complete the game on \"Hard\", with a standard deviation of 1. Another sample (Group 2) of 14 typical players took an average of 2.2 hours to complete the game on \"Easy\", with a standard deviation of 1.2. Calculate the test statistic to test the hypothesis described above, assuming the two population standard deviations are equal.

Solution

  
Calculating the means of each group,              
              
X1 =    6          
X2 =    2.2          
              
Calculating the standard deviations of each group,              
              
s1 =    1          
s2 =    1.2          
              
Thus, the pooled standard deviation is given by              
              
S = sqrt[((n1 - 1)s1^2 + (n2 - 1)(s2^2))/(n1 + n2 - 2)]               
              
As n1 =    10   , n2 =    14  
              
Then              
              
S =    1.122497216          
              
Thus, the standard error of the difference is              
              
Sd = S sqrt (1/n1 + 1/n2) =    0.464758002          
              
As ud = the hypothesized difference between means =    0   , then      
              
t = [X1 - X2 - ud]/Sd =    8.176298175   [ANSWER]