When selecting a computer game an important aspect to consider is the time requi

Question

When selecting a computer game an important aspect to consider is the time required to learn how to play it. The marketing director of Nintendys Inc, hires you as a statistician to design a test based on average learning time. He is pretty sure games A, B and C require the same learning time but wants statistical support to his belief. As a statistician you design a Fisher test and survey 4 customers on game learning time for each of the 3 games. The sample mean learning time for each game are below; The MSE value and degrees of freedom are 3.1 and 9 respectively. Allow for 90% confidence.

Games                           

A - sample mean: 6.8

B - sample mean: 9

C - sample mean: 5.8

a. What is the critical value for the given level of confidence?

b. What is the test statistics for means A & B ? (allow for a difference in values of + or - 0.1)

c. What is the test statistic for means A & C? (allow for a difference in values of + or - 0.1)

d. What is the test statistic for means B & C?  (allow for a difference in values of + or - 0.1)

e. What is your decision (with respect to the null hypotheses) after performing the test for means A & B, A & C and B & C respectively?

f. What is your conclusion after performing these tests with regards to which is different and which is the same?

Explanation / Answer

a) critical value for 90% confidence. and 9 degree of freedom =1.8331

b) test stat for mean A and B =|A-B|/(2*MSE/n)1/2  = 1.7671 (here n=4)

c) test stat for mean A and C =|A-C|/(2*MSE/n)1/2  =0.8032

d)test stat for mean B and C =|B-C|/(2*MSE/n)1/2  =2.5703

E)we can not reject that mean of A and B and A and C are same

we can reject that mean of B and C are same

f) B is dfferent and C. A and C and A and B are same

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