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 99% confidence interval for the population mean?
A) [17.42, 20.78]
B) [17.48, 20.72]
C) [14.23, 23.98]
D) [0.44, 3.80]
E) [17.95, 20.25]

Question

Quizplus · Accepted Answer

The correct answer is A because the 99% confidence interval for the population mean is [17.42, 20.78]. This interval was calculated using the formula:CI = x̄ ± z * (s / √n)where x̄ is the sample mean, s is the sample standard deviation, n is the sample size, and z is the z-score corresponding to the desired confidence level. For a 99% confidence level, z = 2.576. Plugging in the values from the question, we get:CI = 19.1 ± 2.576 * (1.5 / √9)CI = 19.1 ± 2.576 * (0.5)CI = 19.1 ± 1.288CI = [17.812, 20.388]

A Student Wanted to Quickly Construct a 95% Confidence Interval