Answered: In an experiment involving the breaking…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section11.5: Interpreting Data

Problem 1C

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Question

In an experiment involving the breaking strength of a certain type of thread used in personal
flotation devices, one batch of thread was subjected to a heat treatment for 60 seconds and
another batch was treated for 120 seconds. The breaking strengths (in N) of ten threads in each
batch were measured.
60 seconds: 43, 52, 52, 58, 59, 52, 41, 52, 56, 54
12 seconds: 59, 55, 59, 66, 62, 55, 57, 66, 66, 51
Find a 99% confidence interval for the difference in the mean strengths between threads
treated for 60 seconds and those treated for 120 seconds. Assume that the variances for the
two treatments are unequal.

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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