Mathematical Statistics with Applications

7th Edition

ISBN: 9781133384380

Author: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer

Publisher: Cengage Learning US

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Textbook Question

Chapter 8.4, Problem 25E

A study was conducted to compare the mean number of police emergency calls per 8-hour shift in two districts of a large city. Samples of 100 8-hour shifts were randomly selected from the police records for each of the two regions, and the number of emergency calls was recorded for each shift. The sample statistics are given in the following table.

Chapter 8.4, Problem 25E, A study was conducted to compare the mean number of police emergency calls per 8-hour shift in two

a Estimate the difference in the mean number of police emergency calls per 8-hour shift between the two districts in the city.
b Find a bound for the error of estimation.

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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Chapter 8 Solutions

Mathematical Statistics with Applications

Ch. 8.2 - Using the identity ()=[E()]+[E()]=[E()]+B(), Show...Ch. 8.2 - a. If is an unbiased estimator for , what is B()?...Ch. 8.2 - Suppose that is an estimator for a parameter and...Ch. 8.2 - Refer to Exercise 8.1. a. If is an unbiased...Ch. 8.2 - Refer to Exercises 8.1 and consider the unbiased...Ch. 8.2 - Suppose that E(1)=E(2)=, V(1)=12, and V(2)=22....Ch. 8.2 - Consider the situation described in Exercise 8.6....Ch. 8.2 - Suppose that Y1, Y2, Y3 denote a random sample...Ch. 8.2 - Suppose that Y1, Y2,, Yn constitute a random...Ch. 8.2 - The number of breakdowns per week for a type of...

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Solution Summary: The author evaluates the difference in mean number of police emergency calls per 8-hour shift between the two districts in the city.

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Chapter 8 Solutions