If the sample size is held constant,which of the following will produce the widest 90% confidence interval for the population mean difference for a repeated-measures study? A)M_D = 5 with s² = 5 for the difference scores B)M_D = 5 with s² = 10 for the difference scores C)M_D = 3 with s² = 10 for the difference scores D)M_D = 3 with s² = 20 for the difference scores

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Quizplus · Accepted Answer

The confidence interval for the difference in means is calculated as (point estimate) ± t(df, α/2) * (standard error of the difference), where - the point estimate is the sample mean difference - t(df, α/2) is the critical value from the t-distribution, with df degrees of freedom and α/2 significance level (for a 90% confidence interval, α = 0.1 and α/2 = 0.05) - the standard error of the difference is calculated as s / sqrt(n), where s is the sample standard deviation of the difference scores, and n is the sample size To produce the widest confidence interval for the population mean difference, we want the standard error of the difference to be as large as possible, while keeping the sample size constant. Therefore, we want the sample standard deviation of the difference scores to be as large as possible, given the same sample size. Choice D has the largest s² value (20), so it will produce the widest confidence interval.

If the Sample Size Is Held Constant,which of the Following