A 95% confidence interval for $\mu _ { D }$ the true mean difference in paired data, where $\bar { d } = 20 , s _ { D } = 12$ $\text { and } n = 15$ is determined by
A) 20 $\pm$
2)048 (0.80)
B) 20 $\pm$
2)145 (3.098)
C) 20 $\pm$
2)131 (0.894)
D) 20 $\pm$
1)761 (1.118)
E) 20 $\pm$
1)753(1.291)

Question

Quizplus · Accepted Answer

The correct confidence interval is calculated using the formula for the confidence interval of the mean difference in paired data: $\bar{d} \pm t_{\alpha/2, n-1} \times \left(\frac{s_D}{\sqrt{n}}\right)$. Given $\bar{d} = 20$, $s_D = 12$, and $n = 15$, and knowing that for a 95% confidence interval with 14 degrees of freedom (n-1), the t-value (from t-distribution tables) is approximately 2.145, the calculation matches option B.

A 95% Confidence Interval For μD\mu _ { D }μD​ The True Mean Difference in Paired Data, Where

A 95% Confidence Interval For $\mu _ { D }$ The True Mean Difference in Paired Data, Where