To estimate with 95% confidence the average number of kilometres that students living off-campus commute to classes every day, a random sample of 20 students was taken and produced a mean equal to 5.2 km and a standard deviation of 3.05 km. In this case, what would be the approximate value of the upper limit for a 95% confidence interval estimate for the true population mean?
A) 6.63
B) 5.20
C) 3.22
D) 2.15

Question

Quizplus · Accepted Answer

First, we need to calculate the margin of error:
Margin of Error = t-value x (standard deviation/square root of sample size)
Since the sample size is 20, the degrees of freedom is 19 (df=n-1).
For a 95% confidence interval, the t-value with 19 degrees of freedom is 2.093.
Margin of Error = 2.093 x (3.05/sqrt(20)) = 1.922

To find the upper limit of the confidence interval, we add the margin of error to the sample mean:
Upper limit = sample mean + margin of error
Upper limit = 5.2 + 1.922 = 7.122

Therefore, the approximate value of the upper limit for a 95% confidence interval estimate for the true population mean is 6.63 (rounded to two decimal places).

The answer is A.

To Estimate with 95% Confidence the Average Number of Kilometres