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AP Statistics/Unit 5: Sampling Distributions
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Ranking Probabilities for Difference of Means
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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

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