Most video games have several difficulty settings, from \"Easy\" to \"Hard\" (ma

Question

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.

Explanation / Answer

  
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]

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.