THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Independent samples of math scores from students in the U.S.and Europe were collected from normal populations.A sample of 50 students from the U.S.had an average score of 570 while a sample of 50 European students had an average score of 540.The population standard deviations for the average scores of the US and European students are 102 and 115 respectively.
-What is the upper confidence limit of the 95% confidence interval for the difference between the population means?
A)65.65
B)51.73
C)72.61
D)94.23

Question

Quizplus · Accepted Answer

To calculate the upper confidence limit for the difference between the population means, we can use the formula:

Upper limit = (x1 - x2) + z*SE

Where: 
x1 = sample mean for U.S. students = 570 
x2 = sample mean for European students = 540 
z = z-score corresponding to 95% confidence level = 1.96 
SE = standard error of the difference between the means 
SE = sqrt[(s1^2/n1) + (s2^2/n2)] 
s1 = population standard deviation for U.S. students = 102 
s2 = population standard deviation for European students = 115 
n1 = sample size for U.S. students = 50 
n2 = sample size for European students = 50

Plugging in the values, we get: 
SE = sqrt[(102^2/50) + (115^2/50)] = 23.58 
Upper limit = (570 - 540) + 1.96*23.58 = 72.61

Therefore, the upper confidence limit of the 95% confidence interval for the difference between the population means is 72.61.