What is the 95 percent confidence interval for a two-tailed test for the following difference scores: -1, -24, +20, -28, -4?
A) [-12.92, 25.71]
B) [-16.67, 31.47]
C) [-25.72, 12.92]
D) [-31.47, 16.67]

Question

Quizplus · Accepted Answer

The 95% confidence interval for a set of difference scores can be calculated by first finding the mean ($\bar{x}$) and the standard deviation (s) of the difference scores, then using the formula for the confidence interval: $\bar{x} \pm (t_{\alpha/2} \times \frac{s}{\sqrt{n}})$, where $t_{\alpha/2}$ is the t-score that corresponds to the desired confidence level (95% in this case) for a two-tailed test with $n-1$ degrees of freedom (n is the number of scores). For these difference scores (-1, -24, +20, -28, -4), the mean difference is $\bar{x} = -7.4$ and the standard deviation is approximately 20.78. With 4 degrees of freedom (n-1 = 5-1), the t-score for a 95% confidence interval is approximately 2.776. Plugging these values into the formula gives a confidence interval of approximately [-31.47, 16.67], which matches choice D.

What Is the 95 Percent Confidence Interval for a Two-Tailed