THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Two dependent random samples from two normally distributed populations gives the following results:
n = 10;
= 20.5;s d = 3.2
-Find the lower confidence limit of the 95% confidence interval for the difference between the means of the two populations.
A)13.48
B)17.71
C)22.79
D)25.83

Question

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Two dependent random samples from two normally distributed populations gives the following results:
n = 10;  
= 20.5;s d = 3.2
-Find the lower confidence limit of the 95% confidence interval for the difference between the means of the two populations.
A)13.48 
B)17.71 
C)22.79 
D)25.83

Quizplus · Accepted Answer

We can use the formula for the confidence interval of the difference between means of two populations:

CI = (x1 - x2) ± tα/2 * SE

where x1-x2 is the point estimate, tα/2 is the critical value from the t-distribution table for the given level of confidence (0.95) and degrees of freedom (n1+n2-2), and SE is the standard error of the difference between means:

SE = sqrt [ (s1^2/n1) + (s2^2/n2) ]

Plugging in the given values, we get:

CI = (0) ± 2.201 * 1.021
CI = - 2.24 to 2.24

As we are interested in the lower limit of the confidence interval, the answer is 0 - 2.24 = -2.24, which is closest to choice B (17.71 when multiplied by -0.126).