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

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Two independent random samples, each of size 50, are drawn from populations with standard deviations of 8 and 12, respectively. The standard error for the difference in sample means, xˉ1−xˉ2\bar{x}_1 - \bar{x}_2, is calculated as 8250+12250≈2.04\sqrt{\frac{8^2}{50} + \frac{12^2}{50}} \approx 2.04. Assuming the true difference in population means is 0, which of the following correctly ranks the events below in order of increasing probability?

A: The difference in sample means is less than -5.
B: The difference in sample means is greater than 3.
C: The difference in sample means is greater than 0.
D: The difference in sample means is between -2 and 2.

A

A, B, C, D

B

D, B, A, C

C

A, C, B, D

D

B, A, D, C

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