Answered: Nationally, the per capita monthly fuel…

Name: Nationally, the per capita monthly fuel oil bill is $110. A random sam
Uploaded: 2024-03-20T07:07:12.000Z
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Description: Nationally, the per capita monthly fuel oil bill is $110. A random sample of 36 cities in the Southeast average $78, with a standard deviation of $4. Is the difference significant? Summarize your conclusions in a sentence or two.

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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Nationally, the per capita monthly fuel oil bill is $110. A random sample of 36 cities in the Southeast average $78, with a standard deviation of $4. Is the difference significant? Summarize your conclusions in a sentence or two.

Expert Solution

Step 1

Let $μ$ denotes the population mean per capita monthly fuel oil bill. The national per capita monthly fuel oil bill is $110. The hypothesis is,

Null hypothesis:

$H_{0} : μ = $ 110$

Alternative hypothesis:

$H_{a} : μ \neq $ 110$

The test statistic is,

$\begin{array}{rcl} t & = & \frac{\bar{x} - μ}{(\frac{s}{\sqrt{n}})} \\ = & \frac{78 - 110}{(\frac{4}{\sqrt{36}})} \\ = & \frac{- 32}{0.6667} \\ = & - 48 \end{array}$

The test statistic is -48.

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