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AP Statistics/Unit 5: Sampling Distributions
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Probability for Difference in Sample Means

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A researcher compares two treatments. The two populations of reaction times are independent and approximately normally distributed with standard deviations of σ1=0.15\sigma_1 = 0.15 seconds and σ2=0.20\sigma_2 = 0.20 seconds, respectively. If independent random samples of size n1=25n_1 = 25 and n2=36n_2 = 36 are selected, what is the probability that the observed difference in sample means, xˉ1−xˉ2\bar{x}_1 - \bar{x}_2, is within 0.05 seconds of the true difference in population means, μ1−μ2\mu_1 - \mu_2?

A

0.5000

B

0.6826

C

0.9544

D

0.7330

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