Exhibit 10-4
The following information was obtained from independent random samples.
Assume normally distributed populations with equal variances.

-Refer to Exhibit 10-4.The 95% confidence interval for the difference between the two population means is
A)-5.372 to 11.372
B)-5 to 3
C)-4.86 to 10.86
D)-2.65 to 8.65

Question

Exhibit 10-4
The following information was obtained from independent random samples.
Assume normally distributed populations with equal variances.
 
-Refer to Exhibit 10-4.The 95% confidence interval for the difference between the two population means is
A)-5.372 to 11.372 
B)-5 to 3 
C)-4.86 to 10.86 
D)-2.65 to 8.65

Quizplus · Accepted Answer

The confidence interval is calculated as the difference between the two sample means plus or minus the margin of error. The margin of error is calculated as the critical value times the standard error of the difference between the two sample means. The critical value for a 95% confidence interval is 1.96. The standard error of the difference between the two sample means is calculated as the square root of the sum of the variances of the two samples divided by the sample size. The variances of the two samples are given as 10 and 15, and the sample size is 10. Therefore, the standard error of the difference between the two sample means is sqrt((10+15)/10) = 2.24. The margin of error is therefore 1.96 * 2.24 = 4.4. The difference between the two sample means is 3.5. Therefore, the confidence interval is 3.5 +/- 4.4, or -0.9 to 8.9.

Exhibit 10-4 The Following Information Was Obtained from Independent Random Samples