Use the following to answer the question(s) below.
Three brands of AAA batteries are compared to determine if differences in lifetime exist. Each brand is tested in four devices (TV remote, hand-held game, flashlight and digital camera). The experiment is run once for each combination of brand and device. The twelve runs are ordered randomly. The time (in minutes) that each battery lasts under continuous usage is recorded. The partial ANOVA results are as follows:
-The F-statistic for testing whether the three brands of AAA batteries have equal mean lifetimes is
A) 2.96.
B) 1654.89.
C) 0.98.
D) 827.49.
E) 54.67.

Question

Use the following to answer the question(s) below.
Three brands of AAA batteries are compared to determine if differences in lifetime exist. Each brand is tested in four devices (TV remote, hand-held game, flashlight and digital camera). The experiment is run once for each combination of brand and device. The twelve runs are ordered randomly. The time (in minutes) that each battery lasts under continuous usage is recorded. The partial ANOVA results are as follows: 
-The F-statistic for testing whether the three brands of AAA batteries have equal mean lifetimes is
A) 2.96. 
B) 1654.89. 
C) 0.98. 
D) 827.49. 
E) 54.67.

Quizplus · Accepted Answer

The F-statistic is a ratio of variances and typically ranges from 1 to a few tens or hundreds in practical applications. A value of 2.96 is plausible for comparing means across groups, indicating some difference but not an extreme one. Values like 1654.89, 827.49, and 54.67 are unusually high for an F-statistic, suggesting either a very large sample size or extreme differences not typical in such tests. A value of 0.98 would suggest almost no difference between groups, which is also possible but less likely to lead to a significant result if the F-statistic is being calculated.

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