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Name: A tire store advertises that the average price of a new set of their t
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Description: A tire store advertises that the average price of a new set of their tires is only $150. One of their recent customers believes their advertised average is too low – that the true mean price for a set of tires exceeds $150. He plans to carry out a hy

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A tire store advertises that the average price of a new set of their tires is only $150. One of their recent customers believes their advertised average is too low – that the true mean price for a set of tires exceeds $150. He plans to carry out a hypothesis test at α = 0.05. In order to perform the test, the customer took an SRS of 8 sets of tires recently sold. The mean of these sets of tires was x̅ = $156.90 and the standard deviation was s = $11.80.

Suppose the p-value of the test is found to be 0.0715 using statistical software. What is the appropriate conclusion at α = 0.05.

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 + ...

Expert Solution

Step 1

As per the information given, the hypothesis of interest is

$H_{0} : μ = 150 v s H_{1} : μ > 150$ (right-tailed)

under the null hypothesis, the test statistic is

$t_{c a l} = \frac{\bar{x} - μ}{S / \sqrt{n}} ~ t_{n - 1}; S = \sqrt{\frac{1}{n - 1} \sum_{i} {(x_{i} - \bar{x})}^{2}}$

and

p-value = $P (t \geq t_{c a l}) = 0.0715$ > α = 0.05

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