Answered: Some fast-food chains offer a…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter1: Expressions And Functions

Section1.5: Descriptive Modeling And Accuracy

Problem 11PPS

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Some fast-food chains offer a lower-priced combination meal in an effort to attract budget-conscious customers. One chain test-marketed a burger, fries, and drink combination for $4.71. The weekly sales volume for these meals was impressive. Suppose the chain wants to estimate the average amount its customers spent on a meal at their restaurant while this combination offer was in effect. An analyst gathers data from 28 randomly selected customers. The following data represent the sample meal totals.

$6.21	$8.40	$6.50	$7.39	$8.60	$11.65	$8.02	$7.20	$4.25	$10.64
6.28	6.57	6.26	6.80	8.46	12.87	7.67	8.86	6.73	7.08
8.47	7.49	8.19	8.82	10.62	7.83	11.42	12.10

Use these data to construct a 90% confidence interval to estimate the population mean value. Assume the amounts spent are normally distributed.

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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