A student wanted to construct a 95% confidence interval for the mean age of students in her statistics class. She randomly selected nine students. Their mean age was 19.1 years,with a sample 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 will use the t-distribution with n-1 degrees of freedom since the population standard deviation is unknown. We can use the formula:

CI = X̄ ± t*(s/√n)

where:
X̄ = sample mean = 19.1
s = sample standard deviation = 1.5
n = sample size = 9
t = t-score for a 95% confidence level with 8 degrees of freedom (n-1)

Using a t-table or calculator, we find that the t-score is 2.306. Therefore:

CI = 19.1 ± 2.306*(1.5/√9) = 19.1 ± 1.38

The confidence interval ranges from 17.72 (19.1 - 1.38) to 20.48 (19.1 + 1.38). Rounded to two decimal places, the 95% confidence interval for the population mean age is [17.95, 20.25]. Therefore, the best choice is D.

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