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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
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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:

H0:μ=$110

Alternative hypothesis:

Ha:μ$110

The test statistic is,

t=x¯-μsn=78-110436=-320.6667=-48

The test statistic is -48.

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