Question

A certain airline wishes to estimate the mean number of seats that are empty on flights that use 737-airplanes. There are 189189 seats on a 737. To do so, the airline randomly picks n=34n=34 flights. For each flight, the number of empty seats is counted. The data are given below.

46, 40, 58, 59, 44, 46, 51, 47, 37, 49, 49, 50, 44, 42, 47, 49, 46, 49, 62, 56, 51, 40, 50, 60, 50, 59, 43, 51, 45, 49, 54, 54, 44, 58

Data from the sample, are saved in the Download .csv file.

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

X¯¯¯¯=X¯=

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empty seats

S=S=

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empty seats


(b) To construct a confidence interval for the mean number using the T distribution for unoccupied seats on all flights that use 737s, what condition must you hold?

A. The sample size is sufficiently large for the Central Limit Theorem to provide a valid approximation.
B. The number of unoccupied seats can be modeled by the Binomial distribution.
C. The number of unoccupied seats are not normally distributed.
D. That the number of unoccupied seats are normally distributed.

(c) Find a 92% Student T confidence interval for μμ, the mean number of empty seats on this airline's flights that use 737s. Use at least three decimal points for your lower and upper bounds. To avoid rounding errors you should use R-Stuido and not Tables.

Lower Bound ==

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empty seats

Upper Bound ==

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empty seats


(d) Find a 92% confidence interval for μμ, the mean number of empty seats on this airline's flights that use 737s, by Bootstrapping 1000 samples. Use the seed 4748 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(4748);
B=do(1000) * mean(resample(c(46, 40, 58, 59, 44, 46, 51, 47, 37, 49, 49, 50, 44, 42, 47, 49, 46, 49, 62, 56, 51, 40, 50, 60, 50, 59, 43, 51, 45, 49, 54, 54, 44, 58), 34));

Ignore any errors or warnings that show up.

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

Lower Bound ==

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empty seats

Upper Bound ==

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empty seats

Answer 1

The required R code is shown below:

It is clear that the CI based on t-test and the boothstrap CI are quite close.

Hope this was helpful. Please leave back any comment.