Problem

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8
MATH1127: Introduction to Statistics (60022)
Lesson 9.3 Distribution Needed for Hypothesis Testing
Unit $3 C$
The Kyoto Protocol was signed in 1997, and required countries to start reducing their carbon emissions. The protocol became enforceable in February 2005. In 2004, the mean CO2 emission was 4.87 metric tons per capita. In 2010, the CO2 emissions for a random sample of 38 countries were collected. Is there enough evidence to show that the mean CO2 emission is different in 2010 than in 2004? State the random variable, population parameter, and hypotheses.
a. The symbol for the random variable involved in this problem is ?
b. The wording for the random variable in context is as follows:
Select an answer
c. The symbol for the parameter involved in this problem is ?
d. The wording for the parameter in context is as follows:
Select an answer
e. Fill in the correct null and alternative hypotheses:
\[
\begin{array}{l}
H_{0}: \text { ? } ? \vee \\
H_{A}: ? \vee ? \sim
\end{array}
\]
f. A Type I error in the context of this problem would be Select an answer
8. A Type ll error in the context of this problem would be Select an answer

Answer

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Answer

A Type II error in the context of this problem would be failing to conclude that the mean CO2 emission in 2010 is different from 4.87 metric tons per capita when it is actually different.

Steps

Step 1 :The symbol for the random variable involved in this problem is \(X\).

Step 2 :The wording for the random variable in context is: 'The CO2 emissions for a random sample of 38 countries in 2010.'

Step 3 :The symbol for the parameter involved in this problem is \(\mu\), which represents the population mean.

Step 4 :The wording for the parameter in context is: 'The mean CO2 emission in 2004, which was 4.87 metric tons per capita.'

Step 5 :The null and alternative hypotheses are: \[\begin{array}{l} H_{0}: \mu = 4.87 \\ H_{A}: \mu \neq 4.87 \end{array}\]

Step 6 :A Type I error in the context of this problem would be concluding that the mean CO2 emission in 2010 is different from 4.87 metric tons per capita when it is actually the same.

Step 7 :A Type II error in the context of this problem would be failing to conclude that the mean CO2 emission in 2010 is different from 4.87 metric tons per capita when it is actually different.

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