Ranking Probabilities for Difference of Means
Consider two independent samples each of size $$50$$ drawn from populations with standard deviations $$8$$ and $$12$$, respectively. The standard error for the difference in sample means, $$\bar{x}_1 - \bar{x}_2$$, is given by $$\sqrt{(8^2/50) + (12^2/50)} \approx 2.04$$ (assuming a true difference of 0). Rank the following events regarding $$\bar{x}_1 - \bar{x}_2$$ in order of increasing probability:
A: The difference is less than $$-5$$.
B: The difference is greater than $$3$$.
C: The difference is greater than $$0$$.
D: The difference is between $$-2$$ and $$2$$.
Express your answer as an ordering of the event labels (for example, “A, B, C, D”).
A
A, C, B, D
B
B, A, D, C
C
A, B, C, D
D
D, B, A, C
Question Leaderboard
Not enough data yet to show leaderboard.
APFIVE