Question

A airline wishes to estimate the mean number of seats that are empty on flights that use 737-airplanes. There are 189 seats on a plane. To do so, the airline randomly picks n=35 flights. For each flight, the number of empty seats is counted. The data are given below.

38, 42, 44, 42, 40, 45, 37, 31, 33, 36, 35, 39, 37, 37, 43, 38, 41, 27, 33, 35, 37, 46, 32, 35, 35, 42, 37, 41, 29, 40, 44, 34, 34, 41, 29

(a) Find the mean and the standard deviation of this sample. Use at least three decimal places in each answer.

(b) To construct a confidence interval for the mean number using the T distribution for unoccupied seats on all flights, what condition must you hold?

A. That the number of unoccupied seats are normally distributed.

B. The sample size is sufficiently large for the Central Limit Theorem to provide a valid approximation.

C. The number of unoccupied seats can be modeled by the Binomial distribution.

D. The number of unoccupied seats are not normally distributed.

(c) Find a 90% Student T confidence interval for μ, the mean number of empty seats on this airline's flights. Use at least three decimal points for your lower and upper bounds.

Lower Bound =

Upper Bound

(d) Find a 90% confidence interval for μ, the mean number of empty seats on this airline's flights, by Bootstrapping 1000 samples. Use the seed 7775 to ensure that R-Studio "randomly" samples the same "random" samples as this question will expect.

You can do this by including the code, you can copy it into your R-Studio to bootstrap your samples.

RNGkind(sample.kind="Rejection");

set.seed(7775);

B=do(1000) * mean(resample(c(38, 42, 44, 42, 40, 45, 37, 31, 33, 36, 35, 39, 37, 37, 43, 38, 41, 27, 33, 35, 37, 46, 32, 35, 35, 42, 37, 41, 29, 40, 44, 34, 34, 41, 29), 35));

Use at least three decimal points for your lower and upper bounds.

Lower Bound =

Upper Bound =

Answer 1