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 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]

Question

Quizplus · Accepted Answer

The correct answer is A because the 95% 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, z is the z-score corresponding to the desired confidence level, s is the sample standard deviation, and n is the sample size.In this case, x̄ = 19.1, s = 1.5, n = 9, and the 95% confidence level corresponds to a z-score of 1.96. Plugging these values into the formula, we get:CI = 19.1 ± 1.96 * (1.5 / √9)CI = 19.1 ± 1.96 * (0.5)CI = 19.1 ± 0.98CI = [18.12, 20.08]

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