he success of an airline depends heavily on its ability to provide a pleasant customer experience. One dimension of customer service on which airlines compete is on-time arrival. The tables below contains a sample of data from delayed flights showing the number of minutes each delayed flight was late for two different airlines, Company A and Company B.Company A34594330332428530481105010267052837827702790385276 Company B466342336610544283885764532496241363463 Formulate the hypotheses that can be used to test for a difference between the population mean minutes late for delayed flights by these two airlines. (Let ?1 = population mean minutes late for delayed Company A flights and ?2 = population mean minutes late for delayed Company B flights.) What is the sample mean number of minutes late for delayed flights for each of these two airlines? Calculate the test statistic. What is the p-value? Using a 0.05 level of significance, what is your conclusion?

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Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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he success of an airline depends heavily on its ability to provide a pleasant customer experience. One dimension of customer service on which airlines compete is on-time arrival. The tables below contains a sample of data from delayed flights showing the number of minutes each delayed flight was late for two different airlines, Company A and Company B.

Company A

34	59	43	30	3
32	42	85	30	48
110	50	10	26	70
52	83	78	27	70
27	90	38	52	76

Company B

46	63	42	33	66
105	44	28	38	85
76	45	32	49	62
41	36	34	63

Formulate the hypotheses that can be used to test for a difference between the population mean minutes late for delayed flights by these two airlines. (Let ?₁ = population mean minutes late for delayed Company A flights and ?₂ = population mean minutes late for delayed Company B flights.)

What is the sample mean number of minutes late for delayed flights for each of these two airlines?

Calculate the test statistic.

What is the p-value?

Using a 0.05 level of significance, what is your conclusion?

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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