(3 points) A study was conducted comparing the score on the Hopkins Verbal Learn

Question

(3 points) A study was conducted comparing the score on the Hopkins Verbal Learning Test (which measures immediate memory recall) for three different groups of students soccer athletes, athletes who play a sport other than soccer, and non-athletes. Random samples of students from each group were tested, and the summary data appears below. Is there sufficient evidence to conclude that the mean Hopkins score is not the same for the three student groups? Use = 0.05. [Hint: For this problem you will need to use one or more of the defining formulas rather than the short-cut formulas] 4. Sample size (n)Sample meanSample Standard Deviation (s) Group Soccer Athletes Other Athletes Non-Athletes 86 95 53 29.90 30.94 29.32 3.73 5.14 3.78

Explanation / Answer

here null hypothesis:Ho:mean Hopkins score is same for the three students.

Alternate hypothesis:Ha: mean Hopkins score is different for at least 2 of three students.

from above:

for (2,231) degree of freedom and 0.05 level critical value F =3.035

as test statistic 2.64 is not higher than critical value we can not reject null hypothesis

we do not have evidence to conclude that Hopkins score is not the same for the three students.

i ni xi S2i ni*(Xi-Xgrand)2 (ni-1)*S2i soccer 86 29.9 13.913 7.275 1182.597 other 95 30.94 26.420 53.316 2483.442 non-athletes 53 29.32 14.288 40.195 742.997 Grand mean=Xgrand=xi*ni/ni= 30.191 100.786 4409.036 SSG SSE

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