AnswersProbability and Statistics with Applications Honors Sem-2-FL-1210300 2024-2025Estimating the Mean DifferenceQuestion 166933
166933
AssignmentMultiple Select

Estimating the Mean Difference

Question 166933 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)

A 95% confidence interval for the mean difference (Brand A – Brand B) in number of laps completed is (1.04, 4.96). Identify all statements that are correct.

Answer
A
We are 95% confident that the interval from 1.04 to 4.96 captures the true mean difference (Brand A – Brand B) in the number of laps completed.
B
It appears that Brand A office chairs may help teams complete more laps than Brand B chairs in official office-chair races.
C
It appears that Brand B office chairs may help teams complete more laps than Brand A chairs in official office-chair races.
D
We have proven that Brand A chairs will help teams complete between approximately 1 and 5 more laps than if they were to use Brand B chairs.
E
We have proven that teams that use Brand A chairs will beat teams that use Brand B chairs.

Explanation

A confidence interval for the mean difference is interpreted as a range of plausible values for the true mean difference, so A is correct. Since the entire interval (1.04, 4.96) is above zero, the estimated mean difference favors Brand A; this supports the cautious conclusion in B. The interval does not prove that every team will complete a particular number of extra laps or beat another team, so D and E overstate the evidence. C gives the opposite direction.

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