Answered: b) Find a 90% confidence interval for…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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What are the chances your flight will leave on time? To the right are a histogram and summary statistics for the percentage of flights departing on time each month from

2001

thru 2006. There is no evidence of a trend over time. Complete parts (a) through (c) below.

n	72
y	80.5417
s	3.04576

65809505101520OT Departure %# of Months

A histogram with horizontal axis labeled “On Time Departure percentage” from 65 to 95 with bin width of 1 and vertical axis labeled “Number of Months” from 0 to 20 in intervals of 1 contains vertical bars with heights that exhibit behavior from left to right over intervals on the horizontal axis as follows: a steady increase from 1 to 7 on the interval 67 to 81, a fast increase from 7 to 13 on the interval 81 to 82, a fast decrease to 6 on the interval 82 to 83, then a steady decrease from 6 to 0 on the interval 83 to 90; there are no bars on the interval 90 to 95.

a) Check the assumptions and conditions for inference.

Is the independence assumption met?

Yes

Is the randomization condition met or is the sample suitably representative?

Yes

Is the 10% condition met?

Yes

Is the nearly normal condition met?

Yes

b) Find a 90% confidence interval for the true percentage of flights that depart on time.

nothing<μ(OT Departure%)<nothing

(Round to two decimal places as needed.)

c) Interpret this interval for a traveler planning to fly.

Choose the correct answer below.

There is a 90% chance that the true mean monthly percentage of on-time departures is within the interval.

A randomly selected month has a 90% chance of having an on-time departure percentage within the interval.

90% of all months have on-time departure rates within the interval.

We can be 90% confident that the interval contains the true mean monthly percentage of on-time departures.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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