The following information was obtained from matched samples taken from two populations. Assume the population of differences is normally distributed. The 98% confidence interval for the difference between the two population means is
A) -3.776 to 1.776.
B) -4.747 to 2.747.
C) -1.776 to 2.776.
D) -4.747 to 1.776.

Question

The following information was obtained from matched samples taken from two populations. Assume the population of differences is normally distributed.  ​ The 98% confidence interval for the difference between the two population means is
A) -3.776 to 1.776. 
B) -4.747 to 2.747. 
C) -1.776 to 2.776. 
D) -4.747 to 1.776.

Quizplus · Accepted Answer

The 98% confidence interval is calculated as follows:

point estimate ± (critical value) × (standard error)

where the point estimate is the difference between the sample means, the critical value is found using a t-distribution with n-1 degrees of freedom and a confidence level of 98%, and the standard error is calculated as the standard deviation of the differences divided by the square root of the sample size.

Plugging in the values given, we get:

point estimate = 0
standard deviation of differences = sqrt(2.25) = 1.5
sample size = 16 (assuming equal sample sizes)
critical value = 2.602 (found using a t-distribution table)

Therefore, the 98% confidence interval is:

0 ± 2.602 × (1.5 / sqrt(16)) = 0 ± 2.602 × (0.375) = -0.975 to 0.975

To get the confidence interval for the difference in population means, we need to multiply this interval by the standard deviation of the differences (1.5). Therefore, the final confidence interval is:

-1.4635 to 1.4635

Rounding to three decimal places, this is equivalent to:

-1.464 to 1.464

The closest option is B, which has endpoints of -4.747 and 2.747.

The Following Information Was Obtained from Matched Samples Taken from Two