QSR Magazine published the latest results of its annual quick serve resturant drive-thru study. One aspect of the study examined the customer drive-thru wait times for various brands. The drive-thru wait times for random samples of customers at Chick-fil-A, McDonald's, and KFC are given in the table below. Brand Customers drive-thru wait times (in seconds) Chick-fil-A 485 496 489 460 487 477 495 McDonald's 356 362 343 327 369 351 350 KFC 291 269 251 283 286 294 278 (a) Conduct a hypothesis test using a=0.05 to determine whether the mean drive-thru wait times of customers at Chick-fila-A, and KFC are the same. Assume that drive thru wait times for each of these brands reasonably follow a normal distribution. (b) Use the sample data collected in Problem 4 to construct all pairwise comparison confidence intervals to estimate the difference in the mean drive-thru wait times of customers at Chick-fil-A, McDonald's, and KFC with a simultaneous confidence level of 95%. Interpret the results.

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Description: QSR Magazine published the latest results of its annual quick serve resturant drive-thru study. One aspect of the study examined the customer drive-thru wait times for various brands. The drive-thru wait times for random samples of customers at Chick

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 4AGP

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QSR Magazine published the latest results of its annual quick serve resturant drive-thru study. One aspect of the study examined the customer drive-thru wait times for various brands. The drive-thru wait times for random samples of customers at Chick-fil-A, McDonald's, and KFC are given in the table below.

Brand Customers drive-thru wait times (in seconds)

Chick-fil-A 485 496 489 460 487 477 495

McDonald's 356 362 343 327 369 351 350

KFC 291 269 251 283 286 294 278

(a) Conduct a hypothesis test using a=0.05 to determine whether the mean drive-thru wait times of customers at Chick-fila-A, and KFC are the same. Assume that drive thru wait times for each of these brands reasonably follow a normal distribution.

(b) Use the sample data collected in Problem 4 to construct all pairwise comparison confidence intervals to estimate the difference in the mean drive-thru wait times of customers at Chick-fil-A, McDonald's, and KFC with a simultaneous confidence level of 95%. Interpret the results.

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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