You are given the following results of a paired-difference test: = -4.6 s_d = 0.25 N = 16 Construct a 99% confidence interval estimate for the paired difference in mean values. A)-2.912 -------- -2.718 B)-4.784 -------- -4.416 C)-5.241 -------- -4.971 D)-3.141 -------- -2.812

Question

Quizplus · Accepted Answer

To calculate the confidence interval, we can use the formula: 
sample mean ± (t-value)x(standard error of the mean difference)
where t-value is calculated using (n-1) degrees of freedom and alpha level of 0.01, and standard error of the mean difference is calculated by dividing the standard deviation of the differences by the square root of the sample size.

Using the given data, we have:
sample mean = -4.6
standard deviation of differences = 0.25
sample size (n) = 16

The t-value can be found using a t-table or calculator with (n-1) degrees of freedom and alpha level of 0.01. It turns out to be 2.921.

The standard error of the mean difference is calculated as:
0.25 / sqrt(16) = 0.0625

Plugging these values into the formula, we get:
-4.6 ± (2.921)x(0.0625)
= -4.6 ± 0.182

Therefore, the 99% confidence interval estimate for the paired difference in mean values is:
(-4.782, -4.418)

The best choice is (B), as it contains the correct range of values for the confidence interval.

You Are Given the Following Results of a Paired-Difference Test