A student wanted to quickly construct a 95% confidence interval for the average age of students in her statistics class. She randomly selected 9 students. Their average age was 19.1 years with a standard deviation of 1.5 years. What is the 95% confidence interval for the population mean?
A) [0.97, 3.27]
B) [15.64, 22.56]
C) [17.97, 20.23]
D) [17.95, 20.25]
E) [17.42, 20.78]

Question

Quizplus · Accepted Answer

To find the 95% confidence interval, we can use the formula:
CI = x̄ ± t*(s/√n)
where x̄ is the sample mean, s is the sample standard deviation, n is the sample size, and t is the critical value from the t-distribution with n-1 degrees of freedom (8 degrees of freedom in this case, since we have a sample size of 9).
The critical value for a 95% confidence interval and 8 degrees of freedom is t=2.306.
Plugging in the numbers, we get:
CI = 19.1 ± 2.306*(1.5/√9)
CI = 19.1 ± 1.53
CI = [17.57, 20.63]
Therefore, the best choice is D, which is the closest option to our calculated confidence interval.

A Student Wanted to Quickly Construct a 95% Confidence Interval