A student wants to estimate the mean amount of money spent by fellow students on textbooks this semester. She surveys 25 different students and calculates the following 95% confidence interval estimate ofmu,the mean amount spent by all students:124 less than mu less than 156.She interprets this confidence in this way: "There is a 0.95 probability thatmu is between 124 and 156." Is this an appropriate interpretation? Why or why not?

Answered: A student wants to estimate the mean…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section: Chapter Questions

Problem 8CR

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A student wants to estimate the mean amount of money spent by fellow students on textbooks this semester. She surveys 25 different students and calculates the following 95% confidence interval estimate of

the mean amount spent by all students:

124 less than mu less than 156

She interprets this confidence in this way: "There is a 0.95 probability that

is between 124 and 156." Is this an appropriate interpretation? Why or why not?

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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