A video game developer is testing a new game on three different groups. Each group represents adifferent target market for the game. The developer collects scores from a random sample from eachgroup. The results are shown in the table below. Round all answers to 4 decimal places.Group A Group B10115110814998160107112111126Group C101109198186160a. What is the F Statistic?b. What is the p-value?c. At the 10% signific ce level,the scores among theferent groups different?O Yes, there is enough evidence to show that the scores among the groups are statisticallysignificant at the 10% level.O No, there is not enough evidence to show that the scores among the groups are statisticallysignificant at the 10% level.

The given sample observations for the three groups are as follows:Group AGroup BGroup C10115110110814910998160198107112186111126160Part (a) Considering μ1,μ2,μ3 as the average of the groups A, B, and C at the respective population levels, it is set up as follows:H0:μ1=μ2=μ3; the averages of the three groups are indifferent.H1:μ1≠μ2≠μ3; the averages of the three groups are not indifferent.Calculation table:GroupsSample observations; yijTotalA10110898107111T1.=525T1.2=275625B151149160112126T2.=698T2.2=487204C101109198186160T3.=754T3.2=568516Total1977 (=G)1331345The Raw Sum of Squares,RSS=∑i∑jyij2=1012+1082+...+1512+...+1012+...+1602=275743Correction factor, CF=G2n=1977215=260568.6Total Sum of Squares,TSS=RSS−CF=275743−260568.6=15174.4Treatment Sum of Square,SST=T1.2n1+T2.2n1+T3.2n1−CF=2756255+4872045+5685165−260568.6=266269−260568.6=5700.4Now, the Error sum of Squares, SSE=TSS−SST=15174.4−5700.4=9474The test statistic is:F=SST(k−1)SSE(n−k) =5700.43−1947415−3≈3.6101Part (b)The p-value for the F=3.6101 with the distribution degrees of freedom, df1=k−1=3−1=2 and df2=n−k=15−3=12 is obtained using the excel function "F.DIST.RT(F,df1,df2)" as follows:The p-value is 0.0592.Part (c)The decision rule is "reject H0, if p-value≤α".For α=0.10, p-value (0.0592)<α. Thus H0 is rejected.The averages of the three groups are concluded to be not indifferent.(a) The test statistic, F=3.6101.(b) The p-value is 0.0592.(c) Yes, there is enough evidence to show that the scores among the groups are statistically significant at 10% significance level.