THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A dependent random sample from two normally distributed populations gives the following results:
n = 20,
= 26.5,s 2 = 3.2
-What is the lower confidence limit of the 98% confidence interval for the difference between the population means?
A)20.90
B)25.30
C)24.68
D)23.99

Question

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A dependent random sample from two normally distributed populations gives the following results:
n = 20,  
= 26.5,s 2 = 3.2
-What is the lower confidence limit of the 98% confidence interval for the difference between the population means?
A)20.90 
B)25.30 
C)24.68 
D)23.99

Quizplus · Accepted Answer

We need to use the formula for the confidence interval for the difference between means for dependent samples, which is:

CI = (x̄d - tα/2 * (sd / √n), x̄d + tα/2 * (sd / √n))

where:
- x̄d is the sample mean of the differences
- tα/2 is the t-value for a two-tailed test with degrees of freedom = n-1 and alpha = 0.02 (since we want a 98% confidence interval)
- sd is the standard deviation of the differences
- n is the sample size

From the given information, we have:

- x̄d = 26.5
- sd = 3.2
- n = 20

To find the t-value, we need to use a t-table or calculator. For df = n-1 = 19 and alpha = 0.02, we get tα/2 = 2.878.

Plugging in the values, we get:

CI = (26.5 - 2.878 * (3.2 / √20), 26.5 + 2.878 * (3.2 / √20))
   = (24.68, 28.32)

So the lower confidence limit of the 98% confidence interval for the difference between the population means is 24.68. Therefore, the answer is (C).