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Name: A consumer advocacy group is doing a large study on car rental practic
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Description: A consumer advocacy group is doing a large study on car rental practices. Among other things, the consumer group would like to do a statistical test regarding the mean monthly mileage, μ, of cars rented in the U.S. this year. The consumer group has g

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 21E

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A consumer advocacy group is doing a large study on car rental practices. Among other things, the consumer group would like to do a statistical test regarding the mean monthly mileage, μ, of cars rented in the U.S. this year. The consumer group has good reason to believe that the mean monthly mileage of cars rented in the U.S. this year is less than last year's mean, which was 2850 miles.

The group plans to do a statistical test regarding the value of μ. It chooses a random sample of monthly mileages and computes the mean of the sample to be 2700 miles and the standard deviation to be 700 miles.

Based on this information, complete the parts below.

(a) What are the null hypothesis H, and the alternative hypothesis H, that should be used for the test?
H, :0
H :0
(b) Suppose that the group decides not to reject the null hypothesis. What sort of error might it be making?
(Choose one) v
(c) Fill in the blanks to describe the Type I error that could occur if the true mean monthly mileage of cars rented in the
U.S. this year is 2850.
A Type I error would be (Choose one)
v the hypothesis that u is (Choose one)
v (Choose one)
when, in fact, µ is (Choose one)

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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