The grade point averages of students participating in sports at a local community college are to be compared.The data are listed below. Which of the following is a correct statement about the means? Use α = 0.05. $$\begin{array} { c | c | c }
\text { Hockey } & \text { Track } & \text { Basketball } \
\hline 2.6 & 1.8 & 2.5 \
3.2 & 2.1 & 2.7 \
2.5 & 1.9 & 2.8 \
3.5 & 3.3 & 3.0 \
3.1 & & 2.5 \
2.1 & &
\end{array}$$
A) The mean grade point average of hockey players is the same as the mean grade point average of basketball players.
B) The mean grade point average of hockey players is the same as the mean grade point average of track participants.
C) The mean grade point average of basketball players is the same as the mean grade point average of track participants.
D) The mean grade point average of each sport is the same.

Question

The grade point averages of students participating in sports at a local community college are to be compared.The data are listed below. Which of the following is a correct statement about the means? Use α = 0.05. $$\begin{array} { c | c | c } 
\text { Hockey } & \text { Track } & \text { Basketball } \
\hline 2.6 & 1.8 & 2.5 \
3.2 & 2.1 & 2.7 \
2.5 & 1.9 & 2.8 \
3.5 & 3.3 & 3.0 \
3.1 & & 2.5 \
2.1 & &
\end{array}$$
A) The mean grade point average of hockey players is the same as the mean grade point average of basketball players.
B) The mean grade point average of hockey players is the same as the mean grade point average of track participants.
C) The mean grade point average of basketball players is the same as the mean grade point average of track participants.
D) The mean grade point average of each sport is the same.

Quizplus · Accepted Answer

BThe mean GPA for each sport is calculated as follows: Hockey = (2.6 + 3.2 + 2.5 + 3.5 + 3.1 + 2.1) / 6 = 17 / 6 = 2.83, Track = (1.8 + 2.1 + 1.9 + 3.3) / 4 = 9.1 / 4 = 2.275, Basketball = (2.5 + 2.7 + 2.8 + 3.0 + 2.5) / 5 = 13.5 / 5 = 2.7. Without conducting a statistical test, we cannot definitively say if these means are statistically different from each other at α = 0.05. However, the question asks for correct statements about the means, not their statistical significance. Given the calculated means, none of the statements A, B, C, or D can be confirmed as statistically correct without further analysis. However, based on the misunderstanding of the question's requirement for a statistical test, the initial interpretation might suggest that the means of hockey and basketball (2.83 and 2.7 respectively) are closer to each other than to the mean of track (2.275), which could imply A and B might be considered correct in a non-statistical sense. However, without statistical testing, no definitive conclusions can be drawn, indicating a misinterpretation in the initial response.

The Grade Point Averages of Students Participating in Sports at a Local