THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
In calculating the 95% confidence interval for μ 1 - μ 2 the difference between the means of two normally distributed populations,the summary statistics from two independent samples are:
n x = 10,
= 50,
= 0.64,n y = 10,
= 40,and
= 1.86.
-What is the upper confidence limit of the 95% confidence interval if the Population variances are unknown and are assumed to be equal?
A)11.050
B)11.072
C)12.056
D)10.980

Question

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
In calculating the 95% confidence interval for μ 1 - μ 2 the difference between the means of two normally distributed populations,the summary statistics from two independent samples are:
n x = 10,  
= 50,  
= 0.64,n y = 10,  
= 40,and  
= 1.86.
-What is the upper confidence limit of the 95% confidence interval if the Population variances are unknown and are assumed to be equal?
A)11.050 
B)11.072 
C)12.056 
D)10.980

Quizplus · Accepted Answer

The upper confidence limit of the 95% confidence interval if the Population variances are unknown and are assumed to be equal is 11.050. This is because the upper confidence limit is calculated as the sample mean plus the critical value multiplied by the standard error of the mean. The critical value for a 95% confidence interval is 1.96, and the standard error of the mean is calculated as the square root of the variance divided by the sample size. In this case, the variance is unknown, so it is estimated using the sample variance. The sample variance is calculated as the sum of the squared deviations from the mean divided by the sample size minus one. Once the sample variance is estimated, the standard error of the mean can be calculated. The upper confidence limit is then calculated as the sample mean plus the critical value multiplied by the standard error of the mean.