A student wanted to 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]

Question

Quizplus · Accepted Answer

To construct the confidence interval, we can use the formula:

CI = sample mean ± (t-value)*(standard error)

where the standard error is:

standard error = standard deviation / sqrt(sample size)

Looking up the t-value for a 95% confidence interval with 8 degrees of freedom (sample size - 1), we find it to be 2.306.

Plugging in the values, we get:

standard error = 1.5 / sqrt(9) = 0.5
CI = 19.1 ± (2.306)*(0.5) = [17.95, 20.25]

Therefore, the best choice is D.

A Student Wanted to Construct a 95% Confidence Interval for the Average