If you wish to estimate with 95% confidence the average number of miles that students living off-campus commute to classes every day, a random sample of 20 students produced a mean equal to 5.2 miles and a standard deviation of 3.05 miles. Then, the upper limit for a 95% confidence interval estimate for the true population mean is approximately:
A) 3.22
B) 6.63
C) 5.20
D) 2.15
E) 1.96

Question

Quizplus · Accepted Answer

Using the formula for confidence interval with a sample size less than 30, we have:

Upper limit = sample mean + (t-value * standard error)
where t-value for a 95% confidence level with 19 degrees of freedom (df=n-1) is 2.093.

Standard error = standard deviation / square root of sample size
= 3.05 / sqrt(20)
= 0.682

Therefore, upper limit = 5.2 + (2.093 * 0.682)
= 6.63

So, the best choice is B.

If You Wish to Estimate with 95% Confidence the Average