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Name: An insurance actuary claims that the mean footwell intrusions for smal
Uploaded: 2024-03-20T07:07:12.000Z
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Description: An insurance actuary claims that the mean footwell intrusions for small and midsize cars are equal. Crash tests at 40 miles per hour were performed on 12 randomly selected small cars and 17 randomly selected midsize cars. The amount that the footwell

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 22SGR

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An insurance actuary claims that the mean footwell intrusions for small and midsize cars are equal. Crash tests at 40 miles per hour were performed on 12 randomly selected small cars and 17 randomly selected midsize cars. The amount that the footwell intruded on the driver's legs was measured. The mean footwell intrusion for small cars was 10.1 centimeters with a standard deviation of 4.11 centimeters. The mean footwell intrusion for midsized cars was 8.3 centimeters with a standard deviation of 4.02 centimeters. At α=.10, can you reject the insurance actuary's claim? Assum the variances are not equal.

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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