An airline is trying two new boarding procedures Option 1 and Option 2 to load passengers onto their Long Beach (LGB) to San Francisco (SFO) flights. Since Option 1 has more automation the airline suspects that the mean Option 1 loading time is less than the mean Option 2 loading time. To see if this is true the airline selects a random sample of 230 flights from LGB to SFO using Option 1 and records their loading times. The sample mean is found to be 17.7 minutes with a sample standard deviation of 5.2 minutes. They also select an independent random sample of 295 flights from LGB and SFO using Option 2 and record their loading times. The sample mean is found to be 18.3 minutes with a sample standard deviation of 4.1 minutes. Since the sample sizes are quite large it is assumed that the population standard deviation of the loading times using Option 1and the loading times using Option 2can be estimated to be the sample standard deviation values given above. At the 0.05 level of significance is there sufficient evidence to support the claim that the mean Option 1 loading time u1 is less than the mean Option 2 loading time u1 for the airline's flight from LGB to SBO? Perform a one- tailed test. 1. State the null hypothesis Ho and the alternative hypothesis H1? 2. Determine the type of test statistic to use? 3. Find the value of the test statistic? 4. Find the critical value at the 0.05 level of significance? 5. Can we support the claim that the mean Option 1 loading time is less than the mean Option 2 loading time for the airline's flights from LGB to SFO?

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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An airline is trying two new boarding procedures Option 1 and Option 2 to load passengers onto their Long Beach (LGB) to San Francisco (SFO) flights. Since Option 1 has more automation the airline suspects that the mean Option 1 loading time is less than the mean Option 2 loading time. To see if this is true the airline selects a random sample of 230 flights from LGB to SFO using Option 1 and records their loading times. The sample mean is found to be 17.7 minutes with a sample standard deviation of 5.2 minutes. They also select an independent random sample of 295 flights from LGB and SFO using Option 2 and record their loading times. The sample mean is found to be 18.3 minutes with a sample standard deviation of 4.1 minutes. Since the sample sizes are quite large it is assumed that the population standard deviation of the loading times using Option 1and the loading times using Option 2can be estimated to be the sample standard deviation values given above. At the 0.05 level of significance is there sufficient evidence to support the claim that the mean Option 1 loading time u1 is less than the mean Option 2 loading time u1 for the airline's flight from LGB to SBO? Perform a one- tailed test.

1. State the null hypothesis Ho and the alternative hypothesis H1?

2. Determine the type of test statistic to use?

3. Find the value of the test statistic?

4. Find the critical value at the 0.05 level of significance?

5. Can we support the claim that the mean Option 1 loading time is less than the mean Option 2 loading time for the airline's flights from LGB to SFO?

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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