Unoccupied seats on flights cause airlines to lose revenue.Suppose a large airline wants to estimate its average number of unoccupied seats per flight over the past year.225 flight records are randomly selected and the number of unoccupied seats is noted with a sample mean of 11.6 seats and a standard deviation of 4.1 seats.How many flights should we select if we wish to estimate $\mu$ to within 2 seats and be 95% confident?

Question

Quizplus · Accepted Answer

We need to use the formula for sample size calculation for a mean with a known standard deviation:
n = [(zα/2 * σ) / E]^2
where zα/2 = 1.96 (for a 95% confidence interval), σ = 4.1 (the population standard deviation), and E = 2 (the desired margin of error).
Plugging in the values, we get:
n = [(1.96 * 4.1) / 2]^2
n = 16.05
Rounding up to the nearest integer, we need to select 17 flights to estimate the average number of unoccupied seats within 2 seats with 95% confidence. So, the answer is D).

Unoccupied Seats on Flights Cause Airlines to Lose Revenue μ\muμ To Within 2 Seats and Be 95% Confident? A)130 B)65

Unoccupied Seats on Flights Cause Airlines to Lose Revenue $\mu$ To Within 2 Seats and Be 95% Confident?
A)130
B)65