Two separate samples are being used to estimate the population mean difference between two treatment conditions.Which of the following would produce the widest confidence interval? A)n₁ = n₂ = 10 with a pooled variance of 10 B)n₁ = n₂ = 10 with a pooled variance of 100 C)n₁ = n₂ = 20 with a pooled variance of 10 D)n₁ = n₂ = 20 with a pooled variance of 100

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Quizplus · Accepted Answer

The width of a confidence interval is directly proportional to the standard error of the mean, which is inversely proportional to the square root of the sample size. Therefore, the wider confidence interval will be produced by the option with the smallest sample size and the largest pooled variance. In this case, option B has the smallest sample size (n = 10) and the largest pooled variance (100), so it will produce the widest confidence interval.

Two Separate Samples Are Being Used to Estimate the Population