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 11 typical players took an average of 6.3 hours to complete the game on \"Hard\", with a standard deviation of 1.3. Another sample (Group 2) of 12 typical players took an average of 2 hours to complete the game on \"Easy\", with a standard deviation of 1.4.

Calculate the test statistic to test the hypothesis described above, assuming the two population standard deviations are equal.

Hint: Referring to the formulas given in the notes for the hypotheses for difference in means, the value of \"d\" is 2 in this problem.

Solution

Ho: mu1 - mu2=2

Ha: mu1-mu2 not equal to 2

Two tailed test for comparison of means

Mean difference = 4.3

4.3-2 = 2.3

Std error =0.565

t = 4.0715

p=0.0005

This is extremely significant.

Hence difference is not 2.